As many species of living creatures, humans have significant differences between males and females:
1) Primary sex characteristics are the sexual organs, directly involved in reproduction and usually observable already at birth. 
2) Secondary sex characteristics include a number of physiological features, such as body and face shape or facial hair, that develop during puberty. 
3) Different levels of sex hormones in males and females, driving secondary sex characteristics development and affecting, directly or indirectly, the individual's metabolism and behavior.

We could say that these three statements describe criteria for definition of male and female. We may add that a human's previous experience, satisfying or not, contributes to their perception of themselves as a man or a woman. 

While a change of physical characteristics is feasible by means of surgery and, to some extent, hormonal therapy, changing the behavior depends very much on the individual. And the past experience of knowing the individual, by self and by others, cannot be changed and will always to some degree affect the present.

However, in rare cases humans are born with both male and female sexual organs, and may experience abnormal hormone levels during and after puberty. Then our three criteria will be hard to apply, and we would have to rely more on the person's perception by themselves and by others around them.
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