When push comes to shove, especially when the enemy medic is gathering uber behind the front lines, it's time to stop helping your team out and go for the jugular…whether it be killing them all, wasting their time and leading them on chases until they finally kill you (so, they lose nothing apparently, but if three of them chase you for an entire minute, you just robbed the enemy team of two man-minutes), or just plain and simple sabotage. The main thing about pyro is not to be predictable. Will he go around burninating people up front, or will he start punishing the snipers and support with flares, or is he seriously going to charge the Huo Long Heavy from the side and strafe him down despite the health drain? Or is he behind you and you're already dead? You're not the fastest class, the only long range capability is your flares, and to do any decent damage with the flame cone you have to keep the enemy right in the center while you're both moving, and oh yeah…it lags behind, you have to know how to trail the center of the fire over a moving enemy…you have to be a step ahead of them at all times just to maximize your primary weapon.
Last time I checked pyro is the only class with no items to raise max health. Revel in your expendability, bully the engis, medics, and snipers, and sting the power classes from behind, with reflects, with flares, or by jumping in their face while they fire explosives.
If your medic and heavy pair have 5% charge left on the uber and soldiers/demos come in to fuck with them, congratulations, you're up. You can't airblast everything, so you have to block with your body while you try. You can only take between 1 and 3 explosions and you're done. Use that health wisely.
Engi's sentry is down and the enemy team is pushing for the final cart point while an uber medic/heavy advance? Light up the pushers, airblast them away, then go airblast the medic back until you run out of ammo while bodyblocking the heavy's bullets or drawing his fire. If you keep the medic back, the heavy can't advance because of the uber range. Airblast them both if you still have the ammo. You're going to die and the only chance you have is your lazy team pulling together and taking out the burning cart pushers. Shit sucks but they have no chance at all with the uber pair pressing in.
If the cart isn't moving, push it. If it's blocked, clear it. If you can't clear it, light everyone on fire and pick someone to try and finish. Even if you die too soon, there's a 50/50 chance they can't get to health before the afterburn kills them. If you're lucky, a friendly heavy or soldier or two will arrive to mop up the low-health enemies you left behind after you die. Remember, your KtD doesn't matter. That matters less than points or raw kills even. What matters is space, time, and composure. I forgot composure. When your enemy is supposed to be pushing the cart or capping the final point and they're hunting a rat in what they thought was ground they controlled, or defending buildings or bottlenecks from sudden threats, their push is screwed unless someone on their team knows to bypass and has the skill to push solo. Basically anything spy can do, you can do showier. It's just harder and instead of slipping away invisibly, you die as soon as someone manages to nail you down. One good pyro can turn the tide of a control point map without even getting a single assist in the process, just by wasting time, stymying aggression, scattering enemies, wasting ubers.
Did I mention wasting ubers?
If you see a heavy/medic heading towards your team's controlled ground and there's nothing to push them off of to environmental death, engage anyways. Even if you didn't surprise them. Remember, go for the medic. This is even more important than usual. Even if you're getting gunned down quickly and can't get to them, pop off some flares hoping to hit. As soon as the flames touch a medic, especially if you're actually doing some real damage, most of them will pop the uber. They can watch a heavy's giant health pool detachedly, but when it's the uber that's in direct jeopardy with their little health pool, either strategy or panic will usually make them pop the uber. Then they kill you. This is good. By the time the fatass heavy gets where he's going, Gloves of Running Urgently or no, they have what, 20% of the uber left if any? Usually the medic won't even survive long enough to build up another one. Either way, you wasted more of that medic's time than you will waste waiting to respawn and run back to the fighting area.
Don't use noob combos like "airblast + reserve shooter"…just don't.
If you use the flaregun enough to get good and then go demo, you will find it suddenly pretty easy to hit with pipes. Then all you have to do is know your map, think in three dimensions, learn to use angles to take down engis, and practice airfragging with stickies, and you can kick basically unlimited ass with demo.