Why does he stare at me if he already has a girlfriend?

I’ve read that it’s natural for people to get attracted to others while in a relationship, but he stares at me as if he’s never seen a girl before in his life…and sometimes when I’ve talked to him he’ll ask about my weekend, then he’ll tell me about his without mentioning his girlfriend. He never mentions her, at least around me.
He goes out of his way to get my attention, and there was even one time where I told him about a concert I went to over the weekend and he pretty much suggested that he would’ve rather had been at said concert with me instead of whatever he was up to that weekend with his gf (which claimed he couldn’t even remember…yeah right). It’s frustrating because I like him (too?), but I’m not going to break up a relationship so I’ve actually backed off completely, I don’t speak to him anymore or anything. He doesn’t know how I feel and I’m not going to tell him. But if he’s not happy with his current relationship then why stay in it?