Why is it that if people label someone as man or woman (meaning sex) on the internet some people cry "but my gender"?

Maybe its because sex and gender have the same word "Geschlecht" in german (my native language), but if I see a naked man, being sure about his sex, it never even come to my mind thinking he might feel/identify as a woman. Even if this person does and tells me, for me, he would still be a man (identifying as a woman) and i wouldnt label him as a woman when talking about him with others.

I also dont get why some people seem to have a problem with being labeled by their sex. The whole problem about this genderfluid stuff is that every person feels different about themselves and we would need endless labels, so why not stick to what we can geneticly see on the outside - the sex? Its by far more practicable and in my opinion its a more important fact about a person than knowing he/she identifies as a turtlefoxbaby other than he/she has serious mental problems.