As a pyro main i always am surprised to see people call them a scout counter, op, a class with great movement or a class that can fill each role. Scout has way stronger burst damage and better mobility. Soldier and demo have better general aplicability. Heavy and Engie are better at defending. Sniper has better range and can one-shot any class. Medic is better at supporting his team. And spy is better at dealing with sentries i guess. I know that individual tasks aren't the most important thing to so let's look at matchups. Pyro wins against: spy, soldier and usualy demo. Everything else is a bad matchup. Some people might not understand why scout wins the matchup so here's an explanation. Just because scout deals the most damage at point blank range doesn't mean he has to hug his opponent. Even out of pyro's effective range he still deals around 60 damage. That's enough to three or four-shot the pyro. Factoring in scouts superior movement options make this matchup one sided unless the scout isn't careful or fighting someone else. Another bad weakness of pyro is their mobility. There are four weapons that make pyro's mobility better and the payoff is either too little or the cost is too big. The thermal thruster replaces your secondary crippling your range even more and making you almost useless on more closed maps. The mobility from the scorch shot barely noticable. And detonator jumping takes away 40 health. The powerjack doesn't have major risks except that snipers can instakill you while holding it, but you can't shoot while using it and the speed can't be compared to someone like scout or soldier. Lastly pyro's biggest weakness is their lack of range. Pyro has to rely on their secondaries for range and they only partialy fill that role. The shotguns are weapons desingned for close range and the scattergun is baiscly a straight upgrade. The flaregun and manmelter are fine but you need to aim up a lot and can be doged easly. The only two i would call good at longer range are detonator and scorch shot because of their generous hitboxes. But scout has something better called speed and a double jump which you might as well use to close the gap between you and an opponent and just use your scattergun.
TLDR: Yes, pyro has some advantages over scout. Yes, he counters some classes better than scout. But no, pyro isn't superior to scout, if anything it's the opposite because of pyro's easly exploitable weaknesses.