Red, in my opinion, is a pretty good illustration of how a child’s subconscious desires can influence the personality of their imaginary friends. We know from Terrence’s penchant for soap operas that he does have at least an inkling of a soft and sensitive side deep down, and it’s perfectly possible that Red, in many ways, is an embodiment of that. That he ultimately found more sympathy in his supposed enemy Bloo than in his creator is what sealed his loyalties. It also seems to me that Red
does have a mean and violent side of his own but he'll only use it for defensive purposes and when pushed too far, as he finally demonstrated with Terrence. You could argue really that Red inherited a lot from his creator, but that he just channelled these personality traits in completely different ways.
To be honest, Berry’s background isn’t really something I’ve thought about too extensively myself (and it wouldn‘t necessarily have had to involve anything terribly shocking or dramatic like physical abuse to have made her who she was, just what kind of influences she received throughout life), but I can’t really blame her fans for wanting to speculate on the matter, even if it goes beyond what the writers have implied and intended. When you like or take an interest in a particular character, especially one with rather vague background details, you do kind of instinctively want to know more and to get thinking of the possibilities. It's only natural.
