Nah, I'm nitpicking because I truly believe in equality. What's sauce for the goose is sauce for the gander.
If a "women's" gym is the closest to his house and has the equipment he uses (e.g. I didn't know treadmills were gender-specific) then why shouldn't a man go? His money's the same as anyone else's.
The women's gym only exists because the atmosphere at the "open" gym is misogynistic. It's just a workaround. The real solution is to make the "open" gym friendlier. Then having a men-only or women-only gym would be stranger.
If a "women's" gym is the closest to his house and has the equipment he uses (e.g. I didn't know treadmills were gender-specific) then why shouldn't a man go? His money's the same as anyone else's.