Captain falcon seems to only have bad matchups, and seems to have trouble against every other character in the game (at least one disadvantage against every other character).
But I have done some testing, and I came to the conclusion that captain falcon has more pro's than cons against pokemon trainer, wich makes that falcon has the advantage in this matchup.
Pokemon trainer has 3 pokemon (=three different characters to face), but due to the stamina addition (making switching out almost a nescissety) and the fact that when you KO one pokemon, another comes out, and in order to change back into the pokemon they where, they have to switch pokemon twice (or if they just want the next one in line, they switch once) and when they switch, it will mostly mean a free attack. (Good pokemon trainers will not change pokemon close to you, but with falcon's CG on swuirtle and grab release>Uair on ivysaur* Charizard seems the best option, but offcourse, a CG and grab release>arial don't change the whole matchup around) So either don't let the opponent switch, or try to abuse the free hit (don't let the opponent switch without punishment)
With that said, its time to look at the individual pokemon pokemon trainer has:
VS Charizard
Quick overview: Charizard is a large(r) opponent, so hitting/punishing him will not be too hard (especially the punishing). Charizard does not have moves that are very dangerous (altough you must always be carefull, as when he hits he can hit hard) but overall charizard is not that dangerous.
Charizards moves
Neutral A: Charizards Neutral A isn't a real threat. It does not do alot of damage, and it can be punished (without much difficulty).
Ftilt: Charizards Ftilt does 11% damage, wich is quite some damage. But charizards Ftilt is also kind of slow, making punishing it not so difficult.
Dtilt: Charizards Dtilt is quite fast (the attack itself) but it does have some after lag. This move is quite hard to punish, but not impossible offcourse. Still, This is one of Charizards harder moves to deal with.
Utilt: Charizards Utilt is also quite fast, and can hit you multiple times if you're not carefull. This can inflict quite some damage on you, and is also one of the harder moves to punish.
Fsmash: Charizards Fsmash is slow (wich makes it really punishable, with a sweet knee or Bair) but it hits hard when it connects.
Dsmash: Dsmash is quicker than Fsmash, but still not very fast. It is ahrder to punish than Fsmash, but it can still be punished very well.
Usmash: Charizards Usmash can hit you twice, and can surprise you after one or two of charizards Utilts. It does quite some damage, but is very punishable.
Nair: Charizards Nair is not very fast, but not too slow either. It has some after lag wich you can punish though. The move itself has quite some knockback too.
Fair: Fair can be a pain. It can send you flying quite far. But its afterlag can be punished nicely.
Dair: Dair can spike, so beware of that. Other than that, its quite slow and has quite some ending lag.
Uair: Uair is quite fast, and does not ahve alot of ending lag. One of the harder moves to deal with.
neutral b: when caught in Charizards flames, you can counter it easily with an Up b, or just shield it.
side b: Rocksmash hits Hard but it can be punished easily. Just watch out for this one.
Down B: Change pokemon - Make sure/try to punish this with a Dsmash or Fsmash when it happens, or even a sweet knee or falcon punch. (I recommend a smash though, as the timing is not too difficult for a smash)
Up B: Up b is kinda hard to counter, but the ending lag can be used for punishment.
Also note that Charizard can glide and has 3 jumps.
VS Squirtle
Quick overview Captain falcon has a CG on squirtle through a grab release (grab release>regrab) wich can even lead into an offstage falling Uair (grab release>offstage falling Uair) this gives falcon an reliable kill move on squirtle and can rack up damage nicely (by pummeling squirtle during your grab). But Squirtles aerials are quite versatile and can be hard to deal with.
Squirtle's moves:
Neutral A: Neutral A is quite fast and can be hard to get through. It can also hit multiple times if you're not carefull.
Ftilt: squirtles Ftilt is fast. It is not almost impossible to punish. Dodging it will be your best option (or shield grab).
Dtilt: Dtilt can be quite a pain. It is also quite fast and can hit multiple times. It is hard to punish but not ipossible (again, shieldgrab)
Utilt: Is also quite fast and hard to punish. You can get hit with Utilt>Utilt if you aren't carefull.
Fsmash: This move is not very slow, but still punishable. It can do quite some damage if it hits too.
Dsmash: Dsmash is also not very slow, but it can be punished during the actual move. (with a falling Dair for example).
Usmash: This move has quite some knockback, but it also has some after lag wich you can punish.
Nair: This move is quite fast and it autocancels with makes it hard to punish.
Fair: This move is also quite fast with little landing lag. And it has quite some knockback. This is one of the harder moves to deal with.
Dair: Dair can be quite a pain as it can be ahrd to get through, it also has little landing lag to punish.Uair: The move itself is quite fast, but there is a bit of landing lag you can punish. (not much though)
Neutral b: Squirtles water gun can push you away, wich can make you miss an attack. But overall this move is not really a big threat. Still watch out this move doesn't sabotage your recovery though.
Side b: This move can be avoided without too much trouble, and shield grabbing this move also isn't really hard.
up b: The move itself is kinda hard to counter, but the after lag can be punished nicely.
Note that squirtle can pivot mindgame you very well, so be carefull with that. Also note that squirtle can only escape the CG when he lands on a platform above you, try to CG him away from platforms for the best result.
VS Ivysaur
Quick overview:
Ivysaur can be quite difficult to deal with. But the grab release>Uair gives falcon a reliable kill option on ivysaur. Also, as ivysaurs recovery is horrible, make sure you gimp/edghe hog him when you get him offstage.
Ivysaurs moves:
Neutral A: Neutral A can be a pain. Make sure to DI out of it, or jump over ivy and punish.
Ftilt: Ftilt can hit multiple times, but can be punished if you jump over him.
Dtilt: Dtilt is quite fast and hard to punish. But canbe shieldgrabbed without much trouble.
Utilt: Is quite fast, but not unpunishable.
Fsmash: Fsmash can hit hard but it isn't really fast (though not that slow either), but the afterlag can be punished nicely.
Dsmash: Dsmash hits on two sides and is quite fast (yet punishable)
Usmash: this move can KO at high(er) percents. It has quite some startup lag, so avoiding it shouldn't be too hard.
Nair: Nair can hit multiple times and can even spike you (although the spike hard) and can be quite difficult to get through. Also it autocancels, wich makes punishing it harder.
Fair: This move inflicts quite some damage, but it isn't very fast and it has quite some landing lag.
Dair: Dair can spike you, so watch out (as this one can spike hard(er)). It is not a very fast move, and it has qutie some ending lag. Also note that ivy will stop in mid air for a short period of time when he uses this move.
Uair: Uair does quite some damage and it makes ivy go down faster. It has quite some ending lag to punish though.
neutral b: This can rack up damage fast if you aren't carefull. Make sure to DI out of it as soon as possible when you get hit by it. If you don't get hit by it, simply punish ivy during the move.
Forward b: A projectile is always a pain, although some projectiles more than others. Ivy's projectile is not too dangerous, but can still make you approach.
Up B: Ivy's recovery is a tether recovery, so make sure to edghehog him when possible.
Conclusion:
Even though squirtles aerials and some of ivy's moves are dangerous, falcon has a reliable kill option on both, wich falcon rarely has. Also, falcon's speed give him a disadvantage especially against charizard. Falcon can rack up damage on squirtle with a CG, and every grab on ivysaur means a free Uair (wich also racks up damage). Overall falcon has quite some pro's on each of the three pokemon, and as the three pokemon need to be/are used together (wich makes the dangers not even present at all times) falcon can handle this matchup.
I'd say: 55-45 or even 60-40 Captain falcon's advantage.
This post does not matter anymore. It started the matchup discussion, wich was its purpose, and with more knoweldge about the matchup, this post has lost its purpose.
I stand by my point of falcon having an advantage over PT, but this post doesn't give the right reasons. Further posted posts of me give a better image.
