Long story short, after reading several forums not of dA, I came across people who try to compare those with Gender Identity Dysphoria (also known as transgender/sexual individuals) with identifying as animals.  Now, typically i find this argument more readily used as a way of mocking the idea of doing anything to confirm the GID of the individual, and also typically encountered among religious groups (in my case, Catholics in particular) but I will recognize beforehand that it is not exclusive to any particular group.

My question is this: I recognize there's a fallacy in the comparison of identifying with another gender, due to studies i've been shown in neurological identifiers being discovered in the last 5 years, but what is the fallacy of the argument?  How is this an inappropriate comparison and how would it be appropriate to debate against this fallacy (or is it only a perceived fallacy?)
A second, less important question, is if there is any difference in approach depending on the religious debater vs the non.

At this point, I'm considering this more of a lesson on logic use as opposed to trying to cause debate, but discussion on the subject after logic explanation is covered would not be discouraged, perhaps focused on other common arguments against or for GID that are fallacious.