The reality is that love's attitude and action have to go together, because love compels action. That is why to say "I love God" but not reveal that in your actions, gives lie to your statement.
Most people I ask immediately say the opposite is hate. But that's an unthinking answer, and doesn't really work: God is love, but God also hates. So if God is love then love can properly hate.
Many have said the opposite of love is indifference, or apathy. As George Bernard Shaw said "The worst sin toward our fellow creatures is not to hate them, but to be indifferent to them: that's the essence of inhumanity". But that says "the worst sin is indifference", the worst sin (if there is one) is not the opposite of love, it's an offense to love.
Indifference is like the cold, or darkness. You can have a lot of heat, or a little heat, but there's no such thing as cold. Cold does not exist, its only a useful word for the absence of warmth. You can have a lot of light or a little light, but you can't have a lot of dark, only the absence of light. In the same way indifference is not the opposite of love, only the absence of love. If I stop loving, I am indifferent. Indifference is inaction, not an opposite. To find the opposite you have to go through nothing and come out the other side. To go from +1 to -1 I have to go through zero.
Someone said the opposite of love is Satan (thinking perhaps of the statement "God is love"). But to say "God is love" is not the same as saying "love is God". So as love is personified in God, the opposite of love is personified in Satan. (Please note, I am not make a statement of dualism, I am not equating God and Satan. God is way more than Satan.)
So what then is the opposite of love? I think we get trapped by the idea that the answer has to be binary, that if there is a +1 then there is also a -1. This is a problem of language. In English we have one word for love, the Greeks had 4, and I'm sure other languages have many subtleties to capture the sense of this thing called love. English as a language encourages seeing love through the lens of dualism. To even make the statement "there is an opposite of love" is to imply dualism.
So at the very least we might be able to conclude there is no exact opposite of love. This also fits with our understanding that God is love. God created all, and so anything we might conclude to be the opposite of love can at most be a twisted distortion of what God made, arising from our use of free will. We can also conclude that the opposite of love must be exhibited in action, because the absence of something is not an opposite. Love is exhibited in action, with consequence. So we may conclude that the opposite will also have consequence through action.
If we then accept that the opposite of love is not something singular, just as love is not one-dimensional, and, if we accept that like love any opposite also includes action leading to consequence, then how should we look at it?
In one of my middle-of-the-night sleepless moments (do you have those too?) I started working through what I knew love is, and then considering the opposite to those characteristics. This also led to the thought that love is relational, so an opposite would break relationship. Then in the morning I saw two online comments in a forum where I raised this question, and which reinforced my thinking. One wise person pointed me to 1 Corinthians 13, which points to what love is. Another said the opposite was "selfishness", which points to the anti-relational nature.
Well, there's lots of facetious "wisdom" on what love is: cartoons, along with mushy, sentimental, deep, silly, or even stupid statements, and lots of cynical comments. Instead lets go with the source that most people find indisputable (especially if evidenced by how much it is used in wedding services). Here we are, from 1 Corinthians 13, love is, and its opposite:
Does not envy
Does not boast
Does not insist on its own way
Does not rejoice at wrongdoing
Rejoices with the truth
Bears all things
Believes all things*
Hopes all things*
Endures all things*
Impatient: cannot stand being delayed by others
Unkind: unfriendly, ungenerous, unsympathetic
Envies: desires what other have for oneself
Boasts: tries to make oneself more than others
Arrogant: belittles others, egotistical, seeks power
Rude: has no consideration of others, puts personal interests first
Insists on own way: considers self to be more important than others
Irritable: indicative of a sensitive and fragile ego
Resentful: self is be more important and deserving than others
Admires wrongdoing: such as men admiring sexual predators
Fears exposure: desires secrecy and keeping actions private
Objects: fights against personal trials and troubles as if unfair
Is a relativist: makes "truth" to be that which suits
Denial: will not face reality but hides in comforting lies
Dies: when faced with truth, finds it cannot survive
Cannot last: finite, fragile, and ultimately insubstantial
The opposite of love denies reality, it is a pretense that whats real is not true. It is flexible, pliable to suit the needs of the moment, relative. This does not mean the opposite of love has no consequence. To deny something is to try and kill it, to deny truth will have consequence (try deny gravity for a few hours). To be unloving to another can destroy them.
My conclusion: The opposite of love exists only in our exercise of free will when we try to destroy love. Love is attitude in action. The opposite is the anti-attitude in action. Both have consequence: love establishes and affirms truth, reality, and relationship. The opposite seeks to replace truth with lies, reality with unreal fantasy, and relationship with individualism.
* The term "things" as used here, should be read as "reality": those things which actually exist, like truth and gravity, as opposed to the things we only imagine to exist like our lies and pink elephants.