Agree/disagree.

What you're saying here is akin to what I said in Let's Talk About Hate. The true opposite of hate is connection.

But to connect is an action that leads the person you're connecting to feel the emotion of being loved, registering as one of the 7 types of love.

Ergo, apathy is the action that makes the person you're behaving apathetically toward feel the emotion of being hated. It will register in one of ways we experience hate.

Action. Emotion. Reaction.