As a coach in the gym, he naturally has no shortage of beautiful women who love fitness. Naturally, he must contact with them. You should pay attention to observe whether he is also very enthusiastic and ambiguous about other female students. If so, then he just misses you in Doby. If you can tease one, count one. Will there be any results?
If you have a good impression on him and like his career, you might as well be bold. If you just like sports, stick to your bottom line and don't care too much about him. He is enthusiastic about you now because you are his student and his client, and you don't really want to talk about your feelings.