The 'what is a man?' question is interesting especially in context with the transgender question. Men typically framed it as a set of specific behaviors and features. As such across cultures you have these rituals of manhood to graduate a individual into these sets of behaviors. By that definition it can then be argued that anything that acts out those behaviors can be considered a Male, hence Trans FTM have a strong case in so far as they accept this.
With the advent of evolutionary theory and biology, features have been brought into the equation and are treated as the end all be all. Usually you'll see conservatives in argument over the matter utilize the argument by chromosome which established that the only true feature necessary to be categorically male is XY chromosomes. Interestingly by accepting this the behavioral argument goes out of the window and as such the argument of presentation, I am unaware of what this is called but essentially it's centered around expression and representation, becomes quite strong. The LGBT theorist will say sure XY determines sex but by that we can say gender is different and can be expressed in anyway. That is sex and gender are separate categories the former representing a none-variable category determined by a specific feature while the later is a category based on a multitude of variable features and behaviors.