As he doesn't have a girlfriend, the purpose of their going to the gym is not to find a girlfriend, but to find an affair. So when your boyfriend goes to the gym, he doesn't want you to go every time, which means he has such an idea. In fact, I think it is also good for two people to go to the gym to exercise together, and they can encourage each other and encourage each other. Now that he has this idea, I think the relationship between the two people really needs to be reconsidered.
But it doesn't rule out the reason why he doesn't want you to accompany him. Maybe you've always liked taking care of him and always suspected that she didn't trust him that much. In fact, my girlfriend is such a person. She usually answers my phone when she comes home, rummages through my chat records and secretly accesses my chat software to see if there is any suspicious opposite sex. The more he did this, the more disgusted I became, so I did something. I know he is suspicious, but I just don't want him to go.
In fact, two men and women together, if there is no trust, then both of them will be very tired. The other two are not married yet, and both sides are suspected of this. They divorced after marriage, that's for sure. It's better to get together and leave, or change themselves or change him.