It’s kinda wild that women are basically expected to take on all the side effect risk of birth control and no one even questions it unless side effects are actually death (Remember Yaz?). I’m also curious about how blocking vitamin A doesn’t have side effects - don’t I need vitamin A?
Remember that in many societies up until recent times sex outside of marriage was seriously frowned upon but the woman was often punished much more harshly than the man (if the man was even punished at all).
Women, then, needed birth control more than men did because pregnancy had more severe consequences for women than for men. Relying on men to take care of birth control requires the woman to put a lot of trust in the man, who might not have nearly as strong an interest as the woman in that birth control being successful.