No I'm kind of in agreement with him on this one. This isn't you pulling this on a player it's the player pulling it on you. Sure if the player came and talked about it before hand I'd probably let it slide, but if they showed up to the table with an attitude of "see it's in the rules it says I can do it" I'd be a little upset with them.

Worst case they're one of those players that loves finding these kinds of rules loopholes that in most cases are something fun but can a lot of times lead to an attitude of system abuse. Just because the rules say you can doesn't mean you should and I think player intent goes a long way here. Do they want something wacky or gimmicky (which goes against the tone I generally try to push both as a player and DM) or do they show up with a well thought out character that puts a little thought behind the mechanics (such as having a little more mountain goat than horse in their centaur).