What kind of love do you mean? Then 'opposite' isn't always uniquely defined. e.g. the opposite of 3, is it -3 or 1/3 or 9 (on a clock) or something else?... It depends what kind of 'opposite'. What's the opposite of green?
Define love, then define hate and apathy. I use apathy as lack of caring. Kinda like 0 on the number line. I think hate and love should be used sparingly and appropriately. I don't like my kids saying they hate something. I ask that they qualify it as dislike.
I define love (and many will disagree) as self sacrifice for the benefit of another. I define hate as self sacrifice to the detriment of another (again, others will disagree). As others will point out, these are very limited and might not capture the love of a child for a parent, and I'm ok with that. I think we use these terms too loosely in general: "I love my phone" or "I hate my new haircut." I prefer to use "like" or "dislike" in these contexts. I would not self-scrifice to harm my new haircut. However, if I love my home, I will sacrifice my time and effort to make it better.
Theory: Love isn't an emotional state as such. It's best thought of as a mental function that transforms how you frame situations from negative or indifferent reactions into more positive ones. It converts Apathy -> Engagement, Anger -> Forgiveness, Disgust -> Compassion, Fear -> Optimism.
For example, I love my children so I want to be engaged in their lives, I forgive them easily when they make mistakes, I do not think twice about helping them if they vomit or can't make it to the toilet in time, and I am excited and optimistic for their future. For other people, I might not naturally have the same kinds of reactions.
If you buy this definition of love then the opposite would be cynicism, which would produce both apathy and hate depending on the situation.
