Why won't this guy talk to me?

There is this adorable guy at my gym that I can't figure out. Many times I will catch him watching me work out but when I catch his eye he quickly turns away. When I'm taking a class he comes to an area near where I'm working out to do his stretching right behind me though there's plenty of other places he could go to. There have been times when I'm a few feet away from him gathering my things and I've said something to him, acknowledged him, and he'll answer me but won't look at me when he's talking, although I've seen him approach and talk to other girls at the gym, some are married and some aren't, and carry on conversations with them. Sometimes he'll come around me or walk in front of the machine I'm working on almost like he wants me to see him and other times he avoids me completely. I'm pretty sure he's not gay because a girl working next to me on the machines that he talks to said he loves attention from women. I can't tell if he's just shy or if I should stop trying to start conversations with him? I can't read his signals -- sometimes I walk by him and he'll look at me and smile and say hi, and other times he seems to stay far away from me and pretend like I don't exist?
Why won't this guy talk to me?
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