The female equivalent of a vasectomy is getting one's tubes tied (tubal ligation). Chemical contraceptives for men are associated with mood disorders like depression, and there are myriad of health effects from oral contraceptive use in women.
You come across as very liberal. I'm assuming but I doubt you're married. So, I'll refrain from being preachy about celibacy. I don't think you'd gravitate to that kind of message. In any case, when it comes to sexual relations women have the most to lose, especially outside of a stable long-term relationship - marriage. Non-hormonal contraceptives aren't as effective as oral contraceptives, but they pose fewer threats to health. Women probably don't know this but if you are on oral contraceptives you don't menstruate (it's called withdrawal bleeding), as the pill simulates pregnancy. And in truth, men find women on it less attractive compared to when they aren't. That's another story.
Even within a marriage context, women have to put their plans for career advancement on hold to bear children. This actually contributes to the income disparity between men and women. This could be rationalized by putting a high value on motherhood, unfortunately, it isn't compensated. Unless you or your husband is balling having many children is a challenge. Not to mention, you diffuse your attention in several directions if you do. I have a bias toward fewer children as I come from a smaller family, so I'm liberal in that respect. However, conservative so I see celibacy as best outside of marriage.
Why are you surprised? Not all Somalis have large families. And for the record, it's Somali.