Anti-parsers dont have a reason for not wanting a parser because they're human. Humans make mistakes. Sometimes, we'll want to fix our mistakes. Sometimes we'll not. But we want it to be our choice. Being outed, constructively or not, positively or not doesn't make humans feel good. At first. Or later. Either way, when playing a game, especially a game of all things and then being told by a program that your numbers aren't up to snuff, it just doesn't feel good.
Numbers are cold. The first impression a parser gives to someone who's not used to it is "your humanely possible efforts suck" or "Conform to a way it should be played". Again, all this over a game. The other side of this spectrum is something like "thought you could sneak in a get carried? Pls". Either way, its still being outed. And when you're outed by a parser, your immediate control over the game is turned over...to other players.
That's my thought on anti-parsers