I'm not sure why you think that's relevant. (Note - I am not OP.)

Being hypocritical is an indictment at the speaker, not of the speech. The most hypocritical person to ever live may well be completely right about their most hypocritical belief. It's just not relevant to the the validity of the idea.

So why do people constantly try to use it as a counterargument?

It seems especially prevalent in these sorts of discussions, and for some reason it's often used as you did here. You have no idea if they are vegan or not, but somehow the mere suggestion that a single person might not be is seen as some kind of refutation of the importance of animal rights in general.