#10 I completely disagree.
In a lot of situations (e.g. those where pyro is run in the first place), it's extremely hard to beat a pyro 1 on 1. However, your logic (when describing how airblasting can mess up the aim of an opponent due to source engine wizardry, the super fast 2-shot kill, etc.) ignores the possibility of multiple people focusing the pyro. In that regard, his lack of damage output, range or mobility completely cripples him. I don't see how a class can have balance issues when, even in the few instances where he can be useful, he crumbles when more than one class focuses on him.
Yeah, puff+sting or puff+flare might be a faster, more guaranteed kill if pulled off correctly than even direct pipes or close-range scattergun, but the scout has hitscan, can double jump and is fast, and the demo can sticky jump and has mid-range capabilities. All the pyro has is that quick kill, which is extremely avoidable if you just don't fight him on his terms.
That's like saying a heavy is OP because if you run right next to him you'll be gunned down almost instantly. It's meaningless without context.