Why does he flirt SO much with me then always mention girlfriend?

There is a guy I know that stares at me all the time, tries to sit next to me anytime he can and always touches my leg with his or brushes against my arm the entire time. He'll wink at me, and greet me with a sexy hello. He'll also at times ensure I catch him checking out my figure. A lot of times if I dress nice, I'll see him turn around to watch me walking away - I turned around to see him & he looked nervous that I caught him looking. A few times he asks his guy friends near me to ski or out to happy hour & does the indirect invitation to me, "Hey Diana, why don't you join us?" It is strange though, he'll do all these things but yet mention he needs to call his girlfriend all the time when near me. If I bring up something a family member of mine did that was sweet, he'll say his girlfriend is sweet too! I assumed if he was trying this hard he wasn't that enamored with his current relationship, but if he does have a girlfriend he likes, I want nothing to do with this guy. Why does he persist to pursue me all the time? It is driving me crazy since I don't want the distraction if he is in a committed relationship and I don't understand. Yet, I would like him very much if he wasn't. What is up? Why would a guy try so hard for 1 1/2 years if he was in a relationship with someone he cares to bring up incessantly only to me. Usually he brings her up after he has pursued sitting near me etc... I have never seen this before & have dated many guys before.
Updates
+1 y
Per your question, here is the update. In late July/Aug, it kept escalating - one day he kept touching my hand when we talked. I thought that was his segway to make a move. Yet, no! I ignored it to see what he'd do. He just kept talking to me for 40 min. After that, I heard a guy friend tease him about talking to me saying wow, I won't interrupt you when she is around! Since that time, he went on vacation 3 weeks ago and is completely blowing me off! Odd, must not be interested anymore?
Updates
+1 y
Also, one day recently when he was ignoring me, we were in a room with other guys and his photo was brought up on the internet. I said, do you know who that is? :) He said, "Wow, he is handsome". I decided not to say anything. That probably was him fishing for feedback and I didn't grab the bait...probably didn't help the case that he is ignoring me :) oh well...
Why does he flirt SO much with me then always mention girlfriend?
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