Chill bro. That argument seems more shouted than nicely constructed. You are correct that it is to no one's shame that they have no father, as that is no fault of their own, but it is important to bear in mind that, like a victim of a car crash, though not culpable for any injury they bear, a fatherless child will still have issues that they must deal with which are particular to their situation. Although the person you were speaking with seemed to be taking a mocking tone, that does not mean that one who has no father should not consider receiving treatment for any problems that that experience may have caused. But you are correct, there is never a need to try and diagnose someone with fatherlessness. I assume the guy was trying to joke around.
