You just have to be stupid careful the entire match. You can't compete with any aerials and those mixed with off brand DI from a throw can get u ****ed up from either a Fthrow kill or some bs followup that shouldnt work. Any miscalculation that you make will generally get you punished. So maybe peach doesn't punish "hard" but she is consistent.
I'm fairly sure miscalculations will get you punished vs a lot more than just Peach. I'm also not sure how you could possibly DI Peach's F-throw poorly because Peach's has a terrible throw mixup game. It's also very, very easy to DI versus her because of how obvious her combo moves and not-combo moves are, especially when you're not a fast faller or pseudo-fast faller (Sheik, Ganon, some others).
This stems from the fact that M2 doesn't really have options vs peach. He can't actually outcamp peach, maybe with some ridiculous precision of turnip catching and reciprocating while simultaneously dishing out baby shadowballs he could overwhelm her. But in general the projectile games are approximately equal. Of course that is before you factor in all the random skill peach pulls from the ground. Because peach can float, the standard WD>Dtilt is rendered useless(obviously unless she is grounded) and while she is airborn the only legitimate approach that you have is a single baby shadowball; believe it or not, not even the shadowball is guaranteed. Your goal is to force her to drop her float and use M2's standard approach but even then its not completely safe. It wouldn't shock me to see m2 get his tail CC Dsmash. What makes it worse is the nature of the input typically gets M2 in trouble making him take extra damage. Being just a tad late on a platform tech chase can get u Dsmashed for up to 60 percent when you attempt a standard nair from below.
In the same vein of thinking though, it is extremely difficult for Peach to catch Mewtwo. Taj spends a lot of the game vs Armada just shadow balling into teleports and resetting the spacing. Though Peach certainly ***** when she gets in, it takes some serious effort to trap a smart Mewtwo.
Same goes for Iori vs Bladewise if you wanna use an example that isn't best players of the characters or whatever.
Standard WD D-tilt can be rendered "useless" by a whole manner of camping strategies, particularly ones that revolve around the platforms. Since Mewtwo has to have alternative options to get around that crap, he must therefore also have something that works against floats. I have certainly seen Taj stuff Fairs with Nairs and he also seems pretty good at simply making Peach miss because at the end of the day if she's floating relatively high with a Fair or Bair (since we're talking about "priority" moves), it's not hard to teleport through her or move back when she starts coming down. CC grab works well against her weak aerials.
In a similar fashion that m2 changes the way sheik normally plays, Peach kinda does the same for m2.
Samus alters the way a lot of characters play but it doesn't necessarily mean they're disadvantaged against her. Different does not necessarily mean worse it just means "different".
By the edge, fair can kill M2 starting in the neighborhood of 105%. Usmash/Uair can also lead to an early death for m2.
Regarding the Fair, I'm just going to say DI better. Unless you're only playing Yoshi's Story and Pokemon Stadium that percent is ridiculous. No way should that happen on FD, Dreamland, or Battlefield. I'm not sure about FoD.
The next two are true but they're also ludicrously hard for Peach to hit. The former significantly more than the latter. You might as well say that Sheik's tipped U-smash can lead to an early death. You're probably more likely to hit that. Mewtwo should not be above Peach and she really does have no way to set up either move in her entire moveset unless something miraculous happens just because of how she is as a character.
I guess in terms of punishment, Sheik and Peach probably wont instantly get a stock from a single M2 mistake but peach tends to be able to punish M2 more consistently simply because she has sooo much priority and can throw out just about anything.
I'd say Sheik and Peach have very comparable priority. I'd also argue that Sheik's priority moves tend to be faster, which is very useful.
You could say that Peach's are more versatile, I suppose, since she can float them at a variety of heights.
Punishing consistently? That's sort of ill-defined but I'll admit she probably hits him more readily if Mewtwo engages her in combat. But since he spends the bulk of the matchup trying to avoid that...
*shrug*
It's a long game.
Peach is definitely harder to fight than Sheik. M2 also loses his tech chasing, ability to approach with Dtilt and subsequently the ability to CC and come out successful. M2s edgeguarding vs peach is one of his weakest. It is risky enough that Id rather save percent and stay onstage most of the time. Furthermore, M2 cannot punish peach very hard at all. For the most part its high risk low reward. M2's punishes vs Peach are typically half a nair and sometimes a grab or a dtilt[maybe a fair after] and they all do relatively low damage. Because Peach has no lag aerials into jab or downsmash, attacking oos isnt usually an option. Most of this is false vs sheik so naturally Id find the MU a little easier.
Thing is though, you ignore a huge amount of the things Peach can't do to Mewtwo. She can't edgeguard him very effectively. She can't combo him very effectively. She has huge issues catching him and pinning him down. She dies fairly early from U-throw comparably to most characters and her slow movement makes it difficult for her to toss moves out vs his significantly better movement. Particularly if she's playing such a heavy float aerial game, which seems to be what you're getting at.
As for shield pressure: Peach's jabs can definitely be punished. D-smash can also be punished out of shield by a lot of characters if the shield holds but I can imagine that being an issue for Mewtwo. And I'm not sure how he goes about punishing it anyway so I'll grant you that.
However, I don't agree with how easily you disregard all of Sheik's shield pressure. If Sheik doesn't tilt poorly and spaces her aerials I assure you that it is extremely difficult to punish them. There are all sorts of very fun frame traps in Sheik's moveset with low aerials.
I also assure you that simply lobbing out D-tilts isn't easy vs Sheik even if she does lack the means to levitate. Sheik has an excellent shield game, crouch cancel game, platform game, and some very nice SH aerials.