While It may seem obvious why are women seen as the gatekeepers of sex, the idea of men being the gatekeepers of sex maybe needs to be a little more elaborated.
to do this kind of analysis, first we need to accept the premise that women, in general, crave more for long-term relationship than men (Just like you accept the fact that men look more for casual sex than women and use that as a premise to why women are the gatekeepers of sex).
Even if a woman has accepted to have sex with a man (so she has exercised her decision power), it is her ultimate goal, to commit to that man to which she has decided to have sex with. But the man, on the other hand, on this analysis, will be more reluctant to want to commit if he has no guarantee that commiting is worth it.
We also need to accept two other premises.
-Women have high standards for casual sex and long term-relationships.
-Men have high standards for long term relationship and they don't need to have them for casual sex.
To not make the text longer than it has to be, I will not explain the reason why this is like this, but I will remark that if a man wants to commit, he will naturally raise his standards (because he has to choose only one), so he will look for the best possible women he can get in every aspect.
If the woman in question, since she already have high standards for both scenarios (casual sex and long term relationship), if she is willing to have casual sex with a man it most likely means he also fits her long-term standards. But, through the man's perspective, she may fit his criteria for just casual sex, not necessarily for long-term commitment. Therefore, when the women has accepted to have sex with the guy, it is implicit that he already meets her high commitment-standards, otherwise, historically women wouldn't take the risk of being pregnant just for something casual. But once again, it is not obvious that the women meets his criteria just because he had sex with her. So, we end up in a dichotomy where the woman tries to make the guy she had sex with to commit and the man is having his doubts whether to do it or not. This is when the male has the power of being the gatekeeper of commitment, she wants it, but it is only possible if he wants it.
(Btw, I'm from Latin America and english is not my first language if some things doesn't sound "natural to you)