I think a mentor/student relationship is quite different, and is based on something other than what you deem to be 'friendship'. It's for another discussion. However, with the parent/child case, consider that there is a kind of hierarchy, and that that which is lower or higher in the hierarchy is more nurturable than that which is higher or lower in the hierarchy respectively. That is, it is one's nature to nurture to some extent. Place the individual at the top of the hierarchy. The family comes next. Firstly, we help ourselves; because we are all, by definition, self-preservationist. Secondly, we help those closest to us; our family and close friends. Next comes those around us who we would consider to be friends or acquaintances. We may or may not help them, depending on how close we are with them.
Now, it could be said that from a socialist perspective, since the aim of it is to strengthen the bonds of community, we should all help one another regardless of intimacy. But from a natural perspective, humans act, I believe, according to the aforementioned hierarchy. Therefore a socialist act which you seem to be considering in your friendship example would be roaming beyond the confines of human nature. Thus, it all comes down to basic beliefs about how we should act. I'm essentially offering an analogy for how we should act based on how we do act. You're explaining that there is an alternative; that we could act differently to how we act.