True hate, in my opinion, is deep, personal hatred, and I believe that it stems from one emotion: hurt. Love and hate are related, you have to love someone somewhere in your mind before you can hate them, and hate stems from having someone that you love hurt you horribly.
Hate is love distorted and reflected back.
I've never considered love and hate to be opposites, since they can co-exist in one's regard for something. Doesn't one both love and hate their parents from time to time? They're not mutually exclusive so, to me, they're not even the same coin. Love derives from affection, hate derives from anger ... and I'll stop that progression right now before I start sounding like Yoda.
To me, the true opposite of both love and hate is ... apathy
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