I keep hearing American men's rights activists cite the existence of the Selective Service as a major reason why men are more oppressed than women. Oftentimes they conflate it with the draft despite the fact that there has been no draft in the United States in 50 years.

I am against the Selective Service and the draft for both sexes, but at this point the SS is an inconvenience, not a credible threat to every young man's way of life. It is very unlikely that there will be a draft considering the nature of modern warfare. Hypothetically there could be a war, and you could be drafted - but hypothetically the law could be changed to require women to register for the SS, too. It simply isn't relevant to any debate about gender.