AITA for telling a guy to stop "working" on my girlfriend?

So there's this guy in my wife's (25F) gym. He's a bit of a loner, but friendly enough. He constantly works out when I (27M) am there too.<br><br>He's told me he's a personal trainer and spends hours at the gym every day. One day he approached me and asked how long I've been dating my wife. When I told him a year, he said "I can't believe that's ended and I haven't seen you around the last few months." and I assumed he'd lost interest.<br><br>Then one day a few weeks ago, he approached us both and asked if he could have a word with me. I stepped outside with him and he basically said that he really liked my wife, but realised that I would never let them be together and he didn't want to "waste his time" anymore waiting for something that would never happen.<br><br>I told him that was weird and to leave us alone, but he said he meant it and left without talking to my wife.<br><br>The next time we went to the gym, he was standing next to the cardio machines that we usually use. When my wife sat on the treadmill, he sat on the bike next to it and started "working out". He cycles for about 10 minutes, then stops to talk to my wife. She tries to cycle, but he talks over her and interrupts her. He tells her about all the workouts he's done today, about his latest clients and about his day in general.<br><br>He's done this three times now and each time my wife complains about how annoying it is. But whenever I step outside, he tells me he's just trying to "move on" and that he accepts that they're not going to be together.<br><br>Yesterday, I was at the free weights and my wife was on the rowing machine. He was on the machine next to her and started lifting massive weights. I assumed that's what he was doing, but then he started talking to himself and counting out exercises.<br><br>My wife complained to me and I went over to tell him to stop "working out" and just leave her alone. He looked shocked, then said that he was just working and that he had a client coming in a few minutes.<br><br>I told him I didn't care if it was true, and to just leave us alone, then I pushed him towards the door and told him to get out. He went outside and came back with the gym manager, who told me that I was causing a scene and harassing other gym members and that if it happens again I'll be banned from the gym. My wife is mad at me for pushing him and said I overreacted.<br><br>AITA?