@Swaning
Completely disagree with the comments saying people who cheat / are cheaters do love their partners.
They dont. Not really. Not in a way that is worth your time, energy, and commitment. They just like the idea of you hanging on, on manipulating you, of being able to do what they want physically in life (sex with others) and emotionally (manipulating you and probably the person theyre sleeping with).
Stop kidding yourselves, making excuses for shitty behaviour, and wasting your lives. He. Does. Not. Really. Love. You.
Move on.
This post reflects a lack of consensus on what "love" means, I think.
Typically, psychologists will define romantic love as something along the lines of a profound attachment to another person, similar in type to the attachment that you have to your primary caregiver in childhood, but with a sexual element added to it. One of its hallmarks is that the lover seeks out proximity to the loved one, and tries to maintain proximity through various means.
It is a natural thing that the vast majority of human being experience, or can experience.
Even absolutely terrible people with no morals, love other people. Ergo, obviously some people do treat their loved ones terribly, to keep them close to them - people abuse, hit, rape, etc in a twisted attempt to keep the loved one close to them. My exh himself once told me that he "broke my legs to keep me from running away".
It also follows that, many times, the cheater who loves his spurned partner does return, because they want to be closed to their loved one. That's nature. We seek out proximity with those with whom we are bonded.
The problem is that many women imagine that "love" makes a relationship worth saving. But love is actually a very cheap, common thing. The fact that a cheater loves you and perhaps you love him back, doesn't mean that it's worth having a relationship with them. Like @category12 says, there are many things that are MUCH more important than love, when it comes to relationships.