first things first: play a bit of those classes. not enough to get pro, but enough to get an idea on routes a scout or solly will take and how they move/aim. Know your enemy and whatnot. This is really the best advice for anyone wanting to learn how to get better at dealing with a given class.

second, learn your maps. pyro is neither offensive or defensive, but rather support. Pure disruption in an asbestos suit. The reason for this is that the pyro works best by knowing where enemies tend to move and where choke points are. As they have more mobility then you you're to play smart by using a mix of patience and baiting to get enemies to come into a more confined area where they can't jump away and you can either sneak up and incinerate them, airblast them into confusion and burn them up in a more direct confrontation or airblast them off a cliff. knowing where your medkits and supply crates are means less hoofing it back to spawn, a dispenser or a medic and more chances to apply constant pressure the enemy team

flame at an angle. always try to attack while moving at a strange angle so they can't properly aim at you. as the fire is a constant stream if you can place it where they're going to be, they're going to hurt.

pick your fights. Pyro's primary has limited range and his secondary is exactly that: your backup. try to engage the enemy on your terms if possible. crits happen, sure, but engaging on your terms gives you the upper hand and better control of the fight. And pyro's disruption and control is second to none.

don't be afraid to disengage. lighting them on fire and airblasting them away to make space and run away if things get dicey is not being a coward: it's being smart. you're telling them to either expend energy and chase or back off and heal off the damage over time. Any fight you can walk away from is a win, IMO.

with those points out of the way, here's some more specific tips:

Soldiers:
-for the most part, learn to reflect. you'll rarely reflect them all, but you'll rarely need to. reflect the ones that come towards you and scoot out of the indirect ones' AoE. a full Air Strike 8-missile salvo is brutal and highly deadly but survivable if you reflect intelligently.

-Don't go in a shotgun war. they have more HP then you and you're likely to lose if you try to trade blows. shotgun is for if they retreat.

-Look up. Soldiers like to rocket jump and can attack from up high. these attacks can be difficult to return.

-Time your attacks with their jump arcs. Once committed to a rocket jump, it's difficult to turn it another direction, so you can get a good idea where they're going to land. aim your flares, fires or shotguns in that direction rather then flailing and wasting ammo in a mid-arc. if you can git gud though, feel free to clip icarus' wings. he needs to be brought down a peg.

-don't generally try to melee a solly unless you can do so from behind. they have more hp and can trade blows pretty well. that and eating a point-blank rocket without an airblast is harsh.

-Directly killing a soldier will usually occur one of two ways, reflecting a rocket or by bringing them somewhere they can't rocket jump away from and outplaying them. their rockets have the same gap between launches as your airblast, so you can actually juggle them with a mix of airblasts and flamethrower, throwing their aim off.

-a smart soldier can bait out airblasts. even learning a given solly's rocket pattern can be tricky or work against you, and a lot of it is learning shooting animations and intuition, but try to airblast if you can but don't get discouraged if you fail. it happens.

Scouts:
-faster and more mobile then soldiers, scouts are hard to melee, shoot or flamedown, so look at their jumps. like a soldier's rocket jump if you can see the scout, you can probably see where he's going. This allows you to plant flares, buckshots and fire in their path.

-scouts have low hp and a good damage output, so try to engage near a health pack. light them on fire, airblast them away as they go for it, grab it for yourself and you can often either scare them off or leave them to run away and die, barring they're carrying milk. they might try to bring you down but if you can see them, you can juggle them.

-fight while knowing where your walls are. scouts are more mobile then you and you don't want to wind up suddenly hitting a wall and being unable to maneuver. in that regard, cover your exits: keep the jumpy bugger from blocking you off with fire and airblasts. he's got less health but the FaN and his other scatterguns are painful when they bodyshot.

-your own shotgun isn't a bad thing this time around, actually. scout's HP VS yours means he doesn't want to try to trade blows unless he can out maneuver you. use this to your advantage when picking your fights. it also allows you to fight back as scouts can otherwise outgun you by simply staying outside your primary's limited range.