In general women endure the side effects because the penalty for not remaining on birth control is higher. And because we're told those symptoms are "normal" and "to be expected". And because we're expected to accept more responsibility for birth control than men are, in general. The guy carries condoms in his wallet, but in a relationship it's the woman's problem.

But yes, women do quit or change methods because they can't stand the symptoms. I quit the pill because of depression, weight gain, and loss of libido. A friend had a non-hormonal IUD removed because it escalated her monthly menstruation to the level of hemorrhage. I know one who avoids the pill because of blood pressure and cancer risks. I know others who simply endure mood swings, weight gain, etc because they don't want to get pregnant and their boyfriends or husbands loathe condoms.

There's a lot to be fixed on both sides. I think some cultural change is in order. I hope we're able to develop a version of male birth control that doesn't have severe side effects. And I wish someone would invest in research into birth control for women that is safer than what we now have too.