A is the father of B. But B is not the son of A. How’s that possible?

Hello!

This is the standard riddle, probably Bilbo and Gollum asked it one to another :)

It exploits our languages' historical sexism: somebody is by default he. Especially if "he" father has been mentioned already. Also a human being is called "a man" in English.

But "me, your father" may have not only sons, but also daughters. So the answer for this situation is "B is the daughter of A".

Let's consider this situation from the point of view of mathematics (functions, mappings). Denote the set of all people (live or not) as P and define the function F from P to P, F(human) = the farther of this human. This function is defined for every human from P, but it has no inverse function, because not every human is somebody's father.