For those still confused about this: man and woman refer to sex, not "gender". Just like other animals have sexed terms to describe their reproductive role in continuing their species (a vitally important role for any species), such as rooster/hen, ram/ewe, bull/cow, tom/queen, stallion/mare, buck/doe, etc., the same applies to humans.

A man is an adult human male.

A woman is an adult human female.

A boy is a juvenile human male.

A girl is a juvenile human female.

It's really very simple. We can disguise our appearance and present as if a stereotype of the appearance of the other sex, but no mammal can actually change sex. If you are born female you can never become a man, and if you are born male you can never become a woman. By all means feel free to wear whatever clothes you want and modify your body, but you can't change reality.