Most transwomen don't have "female brains" per se, for the simple fact that most have undergone a male puberty, the point at which most of the sexual dimorphism takes place. Studies show that certain regions appear different, even feminized or masculinized for ftm, but we can't conclude that because a brain structure appears feminized, and behaviour appears feminized, that one necessarily has anything to do with the other. One could argue for that being too reductive. The mind -brain connection is poorly understood by science and there are identical twins where one is trans and one is not (at least not yet). So there are likely environmental contributions to ->-bleeped-<-.
Is it a mental illness though? Objectively speaking?
The big point of contention is fundamentally, is the trans identity an essential part of the human being (A) or a non essential pathology (B). As it's highly problematic to call human beings "illnesses". Even if some people who identify as trans are in camp A and others are in camp B, it wouldn't be logical to issue a blanket statement that "->-bleeped-<- is a mental illness." That would be transphobia.