Guys, Why does he sometimes act hot and cold and I feel like he's pushing me away?

We are both in a relationship, but something has drawn us together since the first time we met at work. Common topics and interests, so a colleague also became a personal trainer. We are together and write to each other almost daily, we share photos of cabins where we would like to get away from it all. We wrote messages that suggested something more than a friend, especially hints that we would miss him and that things had "moved somewhere" since the first time we met. Morning and evening messages too, sometimes he first, sometimes I first. When he is away from home, he talks more, when my partner is not home we can also call each other. Once we went inline skating together after work. Later he started touching me more on my sides, arms, back, he patted my thigh a few times, I did the same, but more carefully. Drinking coffee is our time almost after every training and also at work. The topics of our conversations deepened, including about my relationship problems and that's why he doesn't like my partner. The coach has a partner 20 years younger than him, he knows that the relationship with her is not permanent. After one training session, he invited me to lunch. The next day he received a present from me and immediately asked for "at least a hug" and we kissed on the cheek. Then I received a gift from him. Then he wanted to take me from the gym to the car, when we were sitting in his car, he wanted to wish me a happy new year and then he leaned towards me and I felt like he wanted to kiss me. I kissed him on the cheek because I was a little scared and put my arm around his neck. We haven't had a chance to be alone since then, but I feel like it's my turn now. His partner was at training today and he stroked her so nicely that it makes me sad. Is this a sign that he wants to be more than a colleague, coach and friend? We send each other photos of our lives, sometimes with our legs spread out while relaxing, but not intimately. Sometimes he is hot&cold.

Guys, Why does he sometimes act hot and cold and I feel like he's pushing me away?
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