I have seen this statement countless times, because of how relevant love(or at least, like) and hate are to my desire to even survive, it had a reason to come up a lot in conversation. (It doesn't show up as often now because I don't talk about myself as much. Yeah, I seriously used to do even more of that)
Now, I can totally see why indifference would be opposite to love, love has the requirement of caring. In fact, in this case, absolutely everything that involves the requirement to care, is the opposite of indifference. The opposite of indifference is to care.
However there is a part of this that is rarely paid attention to by itself, the denial of hatred as the opposite of love.
When love is not the opposite of hate, due to their shared quality of involving caring about something, why is:
Red the opposite of green? They share the quality of being colors.
Counterclockwise the opposite of clockwise? They are both relevant to direction.
Optimism the opposite of pessimism? They are both a way of looking at things.
Female the opposite of male? That distinction is only meaningful when speaking of a species that includes both as a possibility.
This is not to say that an absolute lack is not considered an opposite, light and darkness, hope and despair, peace and war, those are still opposites from what I recall of the definition.
Red and green, counterclockwise and clockwise, optimism and pessimism, female and male. Despite how they share a trait or nature, they remain opposites. They are opposites due to their contrary qualities, are they not? They are on the other side, even if both sides are on the same thing.
So why is love and hatred dismissed as unable to be the opposite of the other?
When I love(It should be noted that you may not agree with this as being considered love, but that's a different semantic debate to get into), my desire is most relevant to the beloved's emotions, to the point of having the willingness to sacrifice comfort, to the point of which I have attempted to die for the sake of removing my burdensome existence from who I loved(which didn't work because of that person's intervention). When the beloved suffers, I am overwhelmed by dread and worry, a state that corrodes me with anguish and sometimes, even powerlessness. When I am the cause for their suffering, my immediate response is trying to look for a way to provide compensation, and when I cannot, I despair, with guilt and regret decaying my emotions, causing me to lose interest in everything I do. When the beloved is absent, the longer their absence, the more insecure I become, more anxious, more fearful, even...or rather, especially, once they have died. Perhaps if they had reached a heaven which never disappoints, I would be relieved, however, I am left unable to confirm. In the case I am the cause of happiness for my beloved, I am elated and experience a short illusion of satisfaction, after which I become uncertain of if I could successively meet their desired expectations to become the cause of happiness for them again, to the point of which I even fear disappointing them with failure, being reminded of how it feels impossible to make them happy enough, no matter how many costs I pay. I cannot win in the battlefield of love, where the enemies are countless and often difficult to defeat individually, where they will never stop attacking until my defeat. Victory in love is unfulfilling and temporary, failure in it is devastating and permanent, and the last failure known as death has no current means of avoiding yet.
When I hate, my desire is most relevant to my emotions, to the point of demanding my comfort back at any cost to the hated, to the point of which I have wanted to completely destroy the excruciating presence the hated is. When the hated suffers, I am overjoyed, automatically reveling in their distress, filled with amusement and the desire to witness more harm that inflicts them. When I have actively caused their suffering, I feel empowered and want to prevent them from any pleasure they could access, I feel victorious and enthusiastic, their suffering encourages me to attempt to prolong and continue this entertainment known as the pain of who I despise. When the hated is absent, the longer their absence, the more stable I become, more interested in other things, more inclined towards attaining pleasure that is not fueled by harm of an other, particularly when they are dead. At most, I feel upset considering the possibility of them not remaining within an inescapable afterlife full of eternal torture with no salvation. In the case I am the cause of pleasure for the hated, I am disgusted and can even feel defiled by the smallest reasons, being the cause for their happiness is a great failure in me who suffers at any reminder of restrictions I have in depiving them of their happiness, and every instance of when I feel unsatisfied with their lack of enough suffering only encourages me to try more in any way I can without having to pay too much cost. The battlefield of hate is relatively easy, there is usually only one opponent targeted during a session, and the main problem is the choice of weapons that brings the question of which is the most effective. Given enough distraction from it, I can even reach ceasefire unaware. Victory in hatred can often be sufficient until the hated irritates me again, yet failure in it feels cheap and fleeting. When the hated has died, it is a near absolute victory, and there is no way to avoid it.
I want the beloved to be as close to bliss as possible, as removed from even the slightest of discomfort, to an absolute extent, what is only known to be possible is inadequate, and what is considered realistic is unacceptable.
I want the hated to be as close to adversities as possible, as removed from even the slightest of pleasures, even if it may only be within the realm of possibility.
The most effective escape I have from love's adversities is victory in hatred, the most effective escape I have from hatred's failings is love's curse.
I never hate someone I love, I never love someone I hate. (That said, this is mostly due to luck, having never experienced the impression of who I love, or who I hate, being betrayed or contradicted far enough to convert to the status of a hated or of a beloved, never falling to a deception that is revealed to be too far otherwise or an honest that turns to enough deception. There have been cases where I liked or didn't mind someone until I discovered enough about them to hate or love them, though. The extremes just don't convert to the other.)
Love and hatred, with so many possible related differences, with so many possible exclusions and extremes in the other direction, why are they not eligible for being the opposites of each other? Why must their shared trait of including the requirement of caring make them incapable of being contrary to the other?