Alienation and isolation is a recurring theme in a lot of these old Supergirl stories. She was always getting exiled somewhere, or put in positions where she seemed to betray (or was betrayed by) friends or family. It makes sense, I suppose -- psychological trauma is about the only way to challenge a hero who is physically indestructible. And the fear of losing a pet, or being rejected by your loved ones are things that would resonate pretty strongly with kids (or anyone, really). But the net effect was that Supergirl spent an awful lot of time sitting around weeping and moping.