After a previous question that I asked http://mathoverflow.net/questions/31565/request-for-comments-about-a-claimed-simple-proof-of-flt-closed was closed, someone suggested in the comments that I ask another question that is more suited for MO. That question is as follows:

Are there any nontrivial theorems of the form "Method X cannot possibly prove FLT."?

The reason I am asking is because I'd like to know (by deductive reasoning and not relying on 350 years experience) if it is impossible to prove FLT using elementary methods.