I was reading a reread blog covering the Vorkosigan books. They were discussing some secretive biases and prejudice in Betan society that prevent the people who aren't Cordelia from understanding Vor society and I was suddenly reminded of this conversation on the Miles to Go forum about whether the fact that the contraceptive implants were limited to women and herms was secretly sexist. Unfortunately, the forums require registration, and the discussion is a bit longwinded, so I don't really feel up to posting all of the excerpts, but the main discussion gets into how it's stated several times in the books that, in Betan society, the women and hermaphrodites are the only ones mentioned getting the contraceptive implants. Men, as with our current society, are apparently largely exempt from being responsible for any form of contraception short of a physical barrier or avoiding sex. As with many such discussions, it got a bit charged, and I know that we're probably bringing in our own biases, but it seemed like we came down to two theories.
It's a matter of authors writing what they know
The first book in the series was written nearly 30 years ago. Society has long emphasized women as the ones responsible for avoiding pregnancy, as they're the ones who'll have to deal with it while the man can always skip town. Even today, in 2014, there really does not exist a reliable form of male contraception that is reversible without surgical intravention. One would expect a futuristic society that can grow children in uterine replicators, clone organs, and even entirely reverse someone's sex to have overcome such barriers, but it's possible that it really is a more difficult problem than we give it credence. Either way, it might have just never been conceivable to Mrs. Bujold that male contraception would become that easy.
There is an ugly bias at the bottom of Betan egalitarianism
Another possibility, and not even one that's all that unlikely to me, is that the Betan society harbors their own biases which they paper over with their self-image of being an entirely egalitarian society. There's a quote I've run into that first-world countries that they have a tendency to claim to be completely open-minded, but tend to automatically force any person they interact with to conform to their cultural norms. We have hints in A Civil Campaign that the Betan Colony has its ugly underside as per Is Beta Colony less democratic than it seems?.
Ultimately, this may not be something that can be answered definitively, unless Mrs. Bujold plans to address it in later books, but I am curious if anyone has seen better evidence within the books of how this is handled.