You are correct in saying love is like hate but not on different ends of a graph. Love and hate are emotions that are not simplex they are complex. Anger is simplex but attaching that anger onto something and hating that thing is a complex emotion, complex emotions require thought and intent. Hate can be discarded when you decide to not attach your negative emotions onto people, things and ideas. Love is the same, you have a positive emotion and apply it onto someone or something.
We build complex emotional positions in our minds, often without looking at them carefully. Political sides and religious organizations are good examples of ideologies that many people relate to only emotionally.
Simplex emotions like feeling pain can bring about more complex emotions, once we start thinking about why we are in pain we can attache our pain to a cause and begin to hate the cause. Hate is always a decision, so is love. Lust and anger might not require a decision but they are just precursors to more complex chosen emotions.
Having control of what you allow yourself to become emotional about is like driving the car compared to just riding an emotional Rollercoaster. Often I find humour is much more appropriate vs hate, I could hate the other political party or I could just laugh. One is far more powerful. The reality is I can choose my emotions and I believe anyone can, we can't choose the simplex emotions that surprise us due to events but what we do with these simple 'feelings' changes our world. Once we decide to move from anger or resentment to hate we bring it into our world, we own it. Even anger projection can be chosen, you can feel angry but you don't need to project it.
Hate isn't necessary but we will all experience it and should be able to deal with it, being under educated about emotions and how to control your own thinking process can leave you victimized by others who see how to control you, most of the population today is being run by others tugging them about by their emotions. America elected their president based on hate this time around, let's see how well it goes.