Things That Are Not Really The Problem
He’s probably right.
It really does sound like you’re trying to dictate how his character should be played. Unless your group really feels that alignment and the tension it brings is an integral and interesting part of their game, don’t get hung up on it. A lot of people think alignment is dumb; I’m certainly one of them. It’s just not well-defined enough to bother worrying over it that much.
If you must do something...
Change his alignment, but don’t change his mechanics.
The alignment requirement rules are poorly-considered and do not work well for a huge number of tables. Some recognize this, and ignore them, and others don’t, and suffer under them. (some do enjoy them, of course, but your player does not appear to be one of them)
Instead of him losing his martial arts skills (which, let’s be honest, don’t really have a lot to do with how robotic you are),1 have him suffer social repercussions for his actions. Id est, have the monastery kick him out. Maybe make him find some other kind of “rogue monk” to train with in order to continue taking Monk levels (but throw him that plot hook pretty much immediately).
If he’s not a member of a monastery, what justification is there for the alignment restriction in the first place?
1 It’s been pointed out that the Monk does not lose any class features on “falling,” he just can no longer progress in the class. Since Monk itself is an awful class, that’s actually a good thing for the player (he can take Barbarian now! Awesome!), but that’s also irrelevant. The point is that a player character is the player’s character. While the rest of the world should react appropriately to the actions of the character, including a monastery kicking him out or Modrons recognizing him as “not on our side,” he should still be able to take the class he wants. Or, if Monk lost class features, he shouldn’t. Those are terrible rules, and some of the biggest failings of 3.5.
So this answer is: You cannot justify changing a player’s character. You can change how the world reacts to him – everyone can treat him as a known Chaotic individual regardless of what his sheet says. And if they do, magic can affect him as if he were Chaotic and not Lawful. And at that point, you should just say he is Chaotic and not Lawful – but that should only affect how the world interacts with him. Not the character himself.
The Real Problem
Disagreement in the Group
Basically you, and everyone else in your group, apparently, disagree with this guy. You seem to want to say, “we all agree that you’re not Lawful, so you’re not and you’re going to suffer for that, and you have to accept this because insert magic answer here.”
You’re not going to get that answer. Your player does not have to accept this, nor should he. Your group needs to discuss, explicitly, what they expect from the game. Do not consider that conversation complete until you understand exactly how your expectations differ from everyone else’s. If you think you and another player have all the exact same ideas, you aren’t done yet. There will always be differences.
And you have to respect that. Respecting that does not mean you have to accept it, but respect means you have to compromise. Tell him he’s Chaotic, but let him do what he likes with his character, for starters. Turn it into a plot point, have some crazy Slaad martial artist teach him the insane power of Chaos or something. If Drunken Masters can be a thing (and they are), Chaos-fueled martial artists should be utterly unsurprising.
Or, at the very least, have the respect to tell him, up front and without quibbling, that this is a game where he’s not going to get what he wants or expects. He may choose to leave at that point. I probably would. But at least have enough respect for him to tell him so, so he can make that choice.