It's not that people who make a habit a harming others don't love them, it's that they hate themselves. And it's of course possible that there are people incapable of loving (or who don't love the ones that they hurt) others but I think it is altogether more rare.
My ideas about love are tentative, but I'll give it a shot.
I say there are two kinds of love, love and true love.
In short love is a pure emotion that can only be identified by the person who holds it. It has no requirement no explanation, it just is.
True love is more difficult to define.
It is love and more, it is when you've found your soulmate; but it is also when you and that other person are mature enough to carry on a stable happy relationship. I think both members of the relationship have to be truly actualized in that sense, both people must understand the other and what leads to a happy relationship.
And then there is everything in between.
et vu?