Although the Selective Service law is inherently discriminatory — requiring something of men that it doesn’t require of women — it was considered constitutional because women were excluded from combat. Since women wouldn’t be conscripted, they didn’t need to register. Now that women will be joining at least some combat units, Congress eventually must determine how to handle that new reality.
One of Justin Green’s commenters tackles the question:
I’m not sure why we continue to require men to register with selective service. We haven’t had a draft in over 35 years. It’s a lot of paperwork and must be expensive maintaining a system we don’t intend to use. If we want to reinstate the draft, then we can address that at such a time. I suppose it makes sense for women to register as well as men if we are going to continue to require men to participate in this charade.