What is love without hate? It is still love. Love is love and in a world without hate, love is simply love without the existence of hate. In a universe where only light exists, light is still light. We would just never know what darkness is. Because light would be all that we know.
They wouldn't be loving if they didn't know what hate is. By being able to know what hate is, one knows what love is. By knowing what love is, one knows what hate is. If one knows one thing, one knows what the opposite would be.
Perhaps it is because of our imperfect human nature that we are unable to love without hate. Love equals perfect balance while hate is the disruption of that balance. And because we humans can only strive to be perfect while never achieving such a divine state, we are susceptible to hate.
Hatred isn't the only opposite of love, there is also apathy, which is the opposite of both hatred and love, both strong feelings. Love also has its extreme; when taken too far, it can turn into obsession.