Love and hate are opposites. That's why they're alike.
You care what happens to the people you love and to the people you hate.
The people you love are on your mind, and so are the people you hate.
You can feel love in your chest, as you can hate.
The capacity for both is innate.
The Tao Te Ching trains one to see how opposites are alike, yin and yang. Opposites arise together and are part of each other.
A Christian once told me that love and hate are not opposites at all because they are similar. Love and apathy, she* said, are the real opposites. This expectation that opposites not be alike is a hand-me-down from Zoroaster. His dualistic religion portrayed the god of light fighting the god of darkness.
You can divide the world into light and dark.
* Yes, this was an ex-girlfriend. I am a fool for love.