Life isn't so black and white and some people don't have it in their dna (they are missing a trait) that makes them incapable of love.
You can mistreat someone who you love (although it's f! up), it can and does happen.
You can also treat someone right out of basic human decency and not love them. This too can and does happen. It's life.
People can even say they love a person or that their SO is the love of their life and still cheat on them, without a care in the world about what they just did. It's complicated with most people.
I've known a couple where the guy claimed he hated the girl, even had stalking charges brought against her, a standing warrant, and she had to stay away from him - but she fought him tooth and nail and they are now married. She knew he was it, and got him. His actions said he no longer loved her so why get married if that is the case. Did he just fall in love with her antics later? I'm just using this as one example, there are plenty of others.
All I'm saying is that you can do one without the other.
Oh and your statement:
Love is a behavior, not just an emotion Well, most people don't know what love is, they romanticize the hell out of it, but only relegate it to an emotion. Many people don't recognize it's a behavior.
Oprah had talked about this very thing eons ago.