Hmm, why not "férfik"? Is this just irregular or is there a way that I could have predicted this from the form of "férfi"?
Well, "férfi" is a shortened form of "férfiú". So your next question could be "Why not férfiúk?" I don't know the answer to that question.
What function does the "Mi" have in this sentence? Would a more literal translation be "What we are is not boys, but men"?
"Mi" is only there for emphasis, the sentence would work without it, as well. Oh, maybe you are thinking that "Mi" is "What", is that correct? Well, it is not that. It is "We". The two words, "we" and "what" are the same in Hungarian: "mi". Sorry about that. :)