Offensive Pyro in TF2 is a class that depends entirely on how other people play to be effective, and once that's resolved, the Pyro player also has to be pretty good. Basically, an offensive pyro has to rely on the other team being stupid, allowing the Pyro to run straight up to them or not checking corners, and then panicking if lit on fire. The alleged master of close quarters combat, the Pyro lacks two things for offense:
1) The ability to get to the fight. As has been mentioned, the Pyro has low mobility. A medic can run backwards at least as fast as a Pyro can run forwards, and given how bad the hit detection is for fire, this usually means you can't even touch them. Even if you do get them in your flames, the medic will take you down with his syringe gun well before dying. If they use the Blutsauger, they can actually gain health from your attack. Charging in to an enemy line is completely suicidal unless you're playing against fools, as everybody who's been around for a month knows that a Pyro is an easy target on the charge. The health buffed backburner actually allowed Pyros to do what they are supposed to, once. Then people whined about actually having to fight Pyros, and it got taken away.
2) High immediate damage. If you shoot somebody with your primary weapon, as any class in the game except Pyro, you do full damage immediately. Pyros do not do this. As a Pyro, you only deal part of your damage on the spot, and the rest of it slowly thereafter, with afterburn. Afterburn was nerfed in duration by 40% ages ago, and more and more ways to nullify it have been added to the game. Additionally, the flamethrowers are both extremely short range, AND have damage fall off. This means that even at a range where a Pyro can hit you, and you are doing maximum damage based on fall-off (or lack thereof), the Pyro still isn't at potential. The pyro has to be within melee range for their fire to be most effective, at which point it's generally not the best tool. Also, don't get too close. The flamethrower has the same problem it's had since TF2 released - if you get too close to a person or a wall, it just stops working. They unsuccessfully tried to fix that with the Goldrush patch, and haven't been back to it since. People compare afterburn to bleedout, but that is optional for all classes, and is a feature of melee weapons. The pyro has no option for a primary that doesn't rely on this mechanic. Also, bleedout isn't stopped by jarate, milk, or airblasts, like afterburn is. Most pyros would readily trade their afterburn for that same amount of damage upfront, which every single other class has.
Defensive Pyro is not in nearly as bad shape as the offensive Pyro. As an Engy's pet, a Pyro is unrivaled. Problem is, by using an additional player in the backfield, who has minimal long range capability on a good day, your team loses the equation up front. Defensive teams already are generally down a couple on the battle line, because Engineers and Snipers stick back. Those classes do well behind the line, and can lend long range support, so it evens out. Putting a Pyro in the back, however, simply reduces your effective combatants by one.
The airblast is certainly the defining characteristic of a Pyro at present, which is sad. Pyro should equal fire, and fire is just not effective right now, unless combined with something else, like an axtinguisher. The other problem with airblast is the Pyro is effective only at close range, but our defining tool is used to shove people away, which hurts our ability to fight them. Despite all the babies crying about the puff, blast, axtinguisher combo, it actually takes thought and timing to use. Not only do you have to sneak up on the enemy so they don't see you and kill you, not only do you have to use three different weapon functions in close succession at point blank against a more dangerous foe, but you also have to make sure that when you airblast, you're shooting them in to a nearby wall! If you don't do that, or there is no wall, you have to close the distance a second time and try again. You can pull the combo off against a decent player with one puff, but it's extremely rare to survive against a decent player when you have to do it twice.
As far as ubers, Pyro makes a wonderful uber target. It warms my heart to see people in this thread acknowledging that, as I've been left dumbstruck on far too many occasions on the servers by idiot medics loudly stating that Pyros are worthless to uber and I should go change classes. An uber is pretty much the one way to get a Pyro right up to the front line against good players, where he can do what he's designed to do, and it's wonderful. For countering ubers, Airblast is a great tool, though it's not the be-all end-all some people think it is. A good heavy will tear you up before you get a second airblast off (remember, being airblasted doesn't stop him from shooting you), and against another Pyro it's 50/50 who airblasts who. Against a demo uber, it's great, hands down.
In the end though, it comes down to this:
http://www.nerfnow.com/comic/293
http://www.nerfnow.com/comic/294 (read the caption below for this one, too)
Summary/TL:DR -
The Pyro is designed as a psychological class, and his weapons are more about spooking real-life players then about doing in-game damage. The problem is that experienced players in an FPS don't spook. They simply shoot you and move on, sucking up the pittance burning damage, or couple seconds lost from being airblasted. When Kasparov lost to Deep Blue, one thing that cost him was his attempt to use a psychological move against the computer, which just doesn't work. Playing an experienced FPS'r is similar - psychological rarely work.
