My husband is a Biologist and we often have this discussion.
To clarity, male and female are biological terms, man and woman are gender terms.
In biology, males have pollen or sperm and females have ova/eggs.
There is a grey in-between area, for example, snails are both male and female, and some fish such as Wrass can change sex.
In humans, babies can be born as hermaphrodites having both male and female sex organs.
Generally, a human male is unable to change naturally from male to female and have eggs.
So, from a biological point of view, no human male can not become a female. However, in the future, medical advances may male it possible for males to have a womb and produce eggs, but that seems a long way off.
Gender is different and is based on cultural stereotypes of what is associated with being a man or a woman eg Netball and dresses for women and football and trousers for men as an example. The color pink is interesting. It is currently associated with girls, but about 200 years ago, it was a color worn by young boys. I have seen painted portraits of young boys in pink satin trouser suits, so gender stereotypes can change.
Different cultures have their own stereotype of what a woman is. There are also different subcultures within a culture that have their own definition of being a girl/woman.