1. Failing to understand the levels of war and the separation between them
In the study of warfare, planning unfolds across 3 different regimes: Strategic, operational, and tactical. Similar to how the human body is organised, there are cells at one level, tissues at another level, and then organs. The behavior within these regimes is not isotropic, though: Cells do not behave like tissues, and tissues do not behave like organs. They operate at distinct and self contained levels, working at different tempos and with different tasks, but all towards a common goal. Exactly how they interact and co-exist is often mysterious to the public, even among those who are being paid to understand such matters. Laypeople are frequently guilty of ignoring the levels of war (or pretending there is no separation between them), and making some truly groan worthy mistakes in the process. Heres an example: 'The americans lost the phillipines campaign against the japanese, so its not surprising that the commonwealth lost the battle of hong kong against the japanese too.' Statements like this are a dime a dozen on message boards, and they are absolute rubbish. Heres why.
Even though the americans and commonwealth participated in the same war and fought against the same enemy, they operated in different theaters and often used very different tactics while doing so. But that alone isn't what makes this a bad example. The clincher is that it trys to conflate an entire campaign with a single battle, when the two aren't even at the same hierarchical level! Battles can be lost at any time for any number of reasons, but campaigns are only lost after the conclusion of many separate battles. There are qualitative differences involved. Lets take the example in another direction: 'What might have happened if the americans and commonwealth had switched places during these separate conflicts?' Its entirely possible that the obstacles confounding the americans at the operational level would not have been a factor at the tactical level, and that they would have been victorious in place of the commonwealth. The absence of roads, bridges, and railways would seriously disrupt a forces ability to wage a campaign, but it wouldn't impede their ability to win a battle.
2. Failing to understand how battles are actually won
What determines whether or not a force emerges victorious from a battle? Lets devise a scenario. A general meets with his subordinates and decides to arrange a new mission, in order to put his campaign on more secure footing. He settles on a theater of operation, devises a list of objectives, and selects a force which can carry out the mission. The leaders of that force are then briefed, ordered to mobilise their soldiers, get to the staging area, and carry out the mission. Lets say its an infantry battalion trying to dislodge the enemy from a chain of hamlets. What happens next? People know, on an intuitive level, that victory depends on how well a unit can execute fire and maneuver. Subconsciously, they know that the enemy force must be put into a state of shock, which is the only way that battles are decisively won: Hitting them when they are down (and shattering their morale) is what forces them to withdraw from combat. There is nothing revolutionary or cutting edge about this line of thought, humans have been doing it for thousands of years. The problem is that in the last century, so much technology has been introduced that people think the nature of war has somehow changed. Thats not even remotely true.
So far, technology has merely been a vehicle through which humans can better perpetuate violence against each other and establish control. The methods and tactics may change alot over the years, but the overall aim is always the same: Close with and destroy the enemy to achieve a specific objective, relevant to the war at large. So where did everything start going wrong? If you want someone to pin the blame on, the war department is a good place to start. RMA (revolution in military affairs) based doctrines have obscured the ugly realitys of war with nonsense about shock and awe or information superiority, and not surprisingly, it has failed to yield the huge results promised by advocates. But the damage has been done. RMA mindsets have become pervasive, encouraging people to view everything in isolation rather than a spectrum. Officials introduce fancy gadgets and write new doctrine (full of buzzwords), imagining that they now have an army with exponentially increased effectiveness. An army that no dis similarly equipped force can compete with, and will allow them to win wars cheaply and easily by exchanging information and dropping PGMs.
3. Failing to understand what fighting power is
Far too many people are of the opinion that the weapons and equipment used by a force are what determines whether or not it will emerge victorious. Technical comparisons have relevance when you are comparing the same types of branchs against each other, I.E, infantry against infantry, tanks against tanks, but people often go too far with this train of thought. They will dumb down the differences between entire armys (reductionism to the point of absurdity) and judge them solely on the basis of what kindof guns or gear they have, as if militarys are nothing but an inventory of equipment, and wars are just deterministic interplays of men and machines possessing no free will. The lanchester equations gone mad.  When asked how powerful a certain army is, they will make a laughably one dimensional analysis, mention a few pieces of hardware they find especially impressive (ground penetrating radar, bunker busting bombs, digital signals interception, aerial drones, acoustic gunshot detectors, reactive armor, blah blah blah), and announce that the army in question cannot hope to lose with such advanced technology at its disposal. What these sweeping conclusions inevitably lack are any basis in reality.
Techno-centrism not only marginalises the role played by humans within military hierarchys, but also tends to gloss over the fact that individual or group performance depends upon a host of different factors. Humans are not factory made blank states that come with the same features and attributes, nor are the respective hierarchys they work within. There is a long list of important variables, some of which would include: Ambition, training, cohesion, organisation, initiative, command staffs, leadership skills, personnel selection (who gets recruited and how they are promoted), resource allocation, inter-branch cooperation, tooth to tail ratio, discipline and justice, etc. These are the distinct and intangible qualitys which determine whether a military is hard core, or just another paper tiger. All armys that ever existed can be compared on the basis of their fighting power, from those who fought under sargon of akkad to those who fought under adolf hitler. Surprisingly, some of these ancient armys might actually have scored higher than modern armys in a number of key areas. For example, they typically hail from more aggressive and milataristic societys, and have larger numbers of soldiers to support troops. The belief that armys of the past were qualitatively inferior to those that exist today is usually a sign of bad judgement.
4. That advanced technology is a decisive factor
In a simple world where all other things are equal, the more high tech force will hold an advantage. The problem is that all other things aren't equal: The human ability to react and adapt to hostile environments knows no bounds, and high tech equipment can often be mitigated by low tech counter measures. One example of this would be how afghan militants have used wool blankets to mask their presence from sophisticated thermal imagers. Another would be how the serbians turned off their air defense radars whenever they were targeted by anti-radiation missiles, and reactivated them as soon as the threat had passed. These are two examples in a literally endless list! When you get down to it, advanced technology doesn't matter much in a ground war. Offense-defense spirals unfold in a very predictable fashion: One side introduces a major piece of hardware, the other side finds a way to counter it (either by changing their behaviour, or adopting the hardware themselves), and combat then defaults back to fire and maneuver. Major advantages that are afforded through technology are quickly rendered null, and most observers wouldn't be able to explain why. Maybe its because human locomotion is so much better suited to land than to the water or the air?
After all, you don't need an expensive plane or ship to fight on land, you just need a solid pair of legs. Notice that there is no analogue of the infantry to be found in the air force or navy: This can be explained by the fact that legs are ubiquitous amongst humans, whereas wings or flippers aren't (the entry requirements are lower, so to speak). The military implications of this are obvious: Whereas every country in the world could field a sizable army if they felt the need to, only a few could field a sizable navy or air force. There is another factor which prevents hardware from playing as decisive a role on the ground as it does at sea or air: This is the ground itself! Solid landscapes have cluttered features and unique topographys, whereas liquid bodys and gas atmospheres are mostly homogenous and not subject to regional variation. Camouflage and concealment comes more naturally amidst clutter, and this prevents sensors from playing a decisive role. Furthermore, army branchs can only be optimised for certain kinds of environments, and they do very poorly when forced into others. This is why land combat so often resembles a game of rock paper scissors.
5. That air power alone can win wars
The public is far too enamored with the supposed omnipotence of close air support and interdiction. They overestimate the influence it would have in modern conflicts, thinking that there would be numerous repeats of the normandy air campaign, or the ho chi minh trail operations. There are exceptional papers available which demonstrate why air campaigns like those waged during the gulf war were of less military importance than previously believed. Over hyped as they are, CAS and interdiction missions at least have a justifiable purpose in war, which is more than we can say of strategic bombing. Putting it bluntly, air power has no real intrinsic use of its own: It is an establishment that is best suited for assisting the army and making their missions easier. Americans have a particular difficulty coming to grips with this, since their air force was the 1st in the world to become independent and carry out its own operations, even in theaters where there is no land element whatsoever. Its no surprise that fly boys will play cheerleader for every hackneyed air blockade and bombing mission dreamt up by the executive branch, since it justifys their own existence and perpetuate their bloated mythology.
Heres an excerpt from an article by John Guardiano: 'One of the great lessons of recent military history is that wars cannot be won through air power alone; you need boots on the ground. Recall, for instance, the exaggerated claims of “shock and awe” prior to the 2003 liberation of Iraq. Exponents of air power had assured us that the decisive exercise of military power, principally through aerial bombardment, could paralyze the enemy, destroy his will to fight, and render him impotent. In fact, it was only after U.S. soldiers and Marines engaged the enemy in close combat that Iraqi government and Fedayeen forces surrendered and Iraq was liberated. Even then it took additional close combat over several years ─ in Fallujah, Mosul, Najaf, Baghdad, and elsewhere ─ before the military component of the Iraq War was truly won. And Iraq is hardly the only example that proves the crucial necessity of ground forces in modern-day conflicts. In Afghanistan, for instance, U.S. Marines are today engaging the enemy in close-quarters combat to protect the Afghan citizenry. Jets and air ordinance can’t do this; only soldiers and Marines can.'
6. That guerrillas can be defeated using conventional means
Surprise surprise, the public has actually started to catch on to this one by now. Enough asymmetric wars have been fought in the past decade that they cannot help but notice the futility involved in it. Now, its true that most guerilla forces are deficient in weapons and material, and that whenever they go toe to toe with professional armys they are destroyed wholesale. But then, the problem with guerillas is that they rarely commit to a head on battle against a prepared enemy: They stage raids, set up ambushs, and use sabotage or booby traps. Fighting against guerillas is hard because they have no centralised hq, no supply lines, and nothing to distinguish them from civilians. You can't use armored spearheads or artillery bombardments to fight an elusive and disperse enemy: The only way to beat guerillas is to play their own game.  They inevitably tend to suffer far more casualtys than a professional army, and will experience many defeats before they can hope to be victorious. The problem is that loss exchange ratios are only decisive in wars of attrition, and guerillas are far more tolerant of casualtys than their opponents. Moreover, armys can win wars while losing battles, and they can win battles while losing wars.
Heres an excerpt from an article by Robert M. Cassidy: 'First, big powers do not necessarily lose small wars; they simply fail to win them. In fact, they often win many tactical victories on the battlefield. However, in the absence of a threat to survival, the big powers’ failure to quickly and decisively attain their strategic aim causes them to lose domestic support. Second, weaker opponents must be strategically circumspect enough to avoid confronting the great powers symmetrically in conventional wars. History also recounts many examples wherein big powers achieved crushing victories over small powers when the inferior sides were injudicious enough to fight battles or wars according to the big-power paradigm. The Battle of the Pyramids and the Battle of Omdurman provide the most conspicuous examples of primitive militaries facing advanced militaries symmetrically. The Persian Gulf war is the most recent example of an outmatched military force fighting according to it opponent’s preferred paradigm. The same was true for the Italians’ victory in Abyssinia, about which Mao Tse-tung observed that defeat is the inevitable result when semifeudal forces fight positional warfare and pitched battles against modernized forces.'
 These are a set of equations pertaining to napoleanic style armys in close order formations, where numbers and rate of fire determined victory. Needless to say, combat is not that simple or deterministic anymore.
 In case it wasn't clear enough, professional armys cannot defeat guerillas with the same tactics they use against other great powers. They need to use COIN tactics as early in the conflict as possible, which puts a premium on foot soldiers.