Why does a man sometimes stare at me like he is fascinated and sometimes shakes his head almost in disapproval?

Anonymous
He used to playfully tease me, flirt with me, he would eavesdrop or watch me talking to other men, watch me across the room. He started dating another girl but even so he would continue with these behaviours. One time in front of his girlfriend (I don’t think she saw) he turned around in an elevator and looked in my eyes and took my hand, started stroking it with his thumb and looked in my eyes. Last night we were at a book club and I said something which was in no way offensive or distasteful or anything but he looked down and started shaking his head side to side. What was he likely thinking? He would hardly look at me and then when I was talking to another man he stood by us and was glued to his phone like he was communicating with someone else. What does that mean? I have basically told him to keep his distance given that he has a girlfriend but why is he acting like he disapproves of me?
Why does a man sometimes stare at me like he is fascinated and sometimes shakes his head almost in disapproval?
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