He shouldn't. "Man, there are people who mentally are a gender different from their physical sex? I had no idea!" is ignorant. "I I think you call a person with a vagina a woman" is transphobic.
Woman:
An adult female person.
Female:
Of, relating to, or being the sex that bears young or produces eggs.
Phobia:
An exaggerated, usually inexplicable or illogical fear of a particular object, class of objects, or situation.
Now, I'm not saying the dictionary definitions aren't dated and shouldn't be changed. I am however going to say that a person using dictionary definitions is
not acting in an exaggerated, inexplicable, or illogical manner. They are most likely acting in a manner that is consistent with their existing knowledge and past experiences, and it's simply a case that those experiences have been insufficient to provide them the necessary context to understand why what they're doing or saying is wrong.
That is to say, they are being:
Ignorant:
Lacking knowledge or information.
Now, if you want to say that I'm being pedantic and should understand that we're using the
colloquial version of "transphobic" rather than a literal interpretation, that's a fair cop. I would say, however, that
colloquially "transphobic" is the lingual equivalent to "racist" and is not a word you should be throwing out whenever someone expresses an ill-informed opinion.
A person who doesn't understand why Affirmative Action has been necessary isn't necessarily a "racist", they could and probably are simply lacking full understanding of the socio-economic realities of the situation. A person who doesn't understand how important the issue of biological gender versus gender identification is most likely isn't "transphobic", they're probably just not educated on the topic or at worst an insensitive prick. (Which is bad, but not a
pathological condition.)
More to the point, the worst problem facing the transgender community is the simple fact that most people are completely unaware of gender dysphoria as a condition and the related issues people with it face. Most of them would probably be willing to learn, but not if you go around slinging invectives at every person who doesn't enter the conversation fully-educated and tolerant. Promoting tolerance is a matter of finding people who are willing to listen and engaging with them, not shouting down voices of dissent as loudly as possible.
I'm guessing, based on the fact that Mike (whether he realized it or not) had transgendered individuals in his peer group, that someone actually did approach him in a reasonable manner and explain to him why what he said was needlessly offensive. It probably just took a hundred times as long for it to actually "take" thanks to the thousand people who were instead shouting "fuck you transphobic cis-scum" while someone was trying to walk him through it.