Girls, why he act jealous when I'm around her?

I noticed A girl at the gym that I see every weekend. At first I would check her out but she wouldn't look back at me too much.

But then she would steal glances every so often more when I'm not looking. One of the personal trainers, he's an older guy and myself and him are usually friendly and cat often, he was giving her a ‘free’ session.

I was training near them , and she kept stealing a few glances looking at me and smiled to herself a little while I walked passed. He was trying to talk to her. He kept looking at me, ever since he doesn't say hello or talk to me anymore.

Then I saw her in a local store, she walked passed me and smiled and I smiled back. Days after she was in the gym again, and she would smile but couldn't make eye contact so would look to the ground.

Well this week I was training in the gym again. He walked in to give her another “free” training session. He saw me working out near her, and he instantly looked annoyed that I was near her and proceeded to talk with her.

He didn't say hi to me which is out of the ordinary, and he gave her the “free” session. So now I kind of avoid her a bit.
When I left the gym he was in the parking lot talking to her near her car. She kept looking and then he kept looking at me.

I don't get why he is now acting jealous or like I am threatening is “game plan”. I never spoke to her, I don't know her. She smiled at me in the store but in the gym she smiles and looks to the ground. Although, once when I was around I believe she kept looking at me a few times.

1) why does he act odd with me now and appear to have an issue with me being anywhere near her?

2) is she even interested in me, and why she smile at me when passing but then act shy in the gym by smiling and avoiding eye contact, and keep sneaking looks at me?

3) I feel like he uses his personal training role to try and pull Or flirt with women? He is a slightly older guy

Ps I am 27 not 30-35.
Girls, why he act jealous when I'm around her?
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