Selective Service is unconstitutional
There has not been a military draft in the United States since the Vietnam War in the 1960's and 1970's, but there is still a mechanism in place by which the U.S. government could institute a draft if it decides to do so. Selective Service has come and gone since President Woodrow Wilson signed the original act during World War I, but its current iteration has been in place since being re-established by President Jimmy Carter in 1980. All male American citizens, along with some male non-citizens, between the ages of 18-25 must register with the Selective Service for a potential military draft under the current law.
The law has been challenged on the basis that it only applies to males and that it must apply equally to females as well, but these challenges have not been upheld. There have also been recent legislative efforts to amend the law to make it apply to females as well as males, but this has also not happened as of this writing.
While it's certainly true that it's hypocritical and unequal for only men to be required by law to register with the Selective Service, that is beside the point. The point is that forcing any person, male or female, to register for a potential draft, or to institute a draft at all, is unconstitutional. The Thirteenth Amendment to the United States Constitution explicitly states:
Neither slavery nor involuntary servitude, except as a punishment for crime whereof the party shall have been duly convicted, shall exist within the United States, or any place subject to their jurisdiction.
What is a military draft if not involuntary servitude? You are forcing a person to join the military and serve in a war against their will. The Thirteenth Amendment abolished slavery in the United States after the Civil War, but it also clearly applies to a military draft. The U.S. Supreme Court, however, has ruled that this is not the case. In Butler v. Perry, the Court stated:
Utilizing the language of the ordinance of 1787, the 13th Amendment declares that neither slavery nor involuntary servitude shall exist. This Amendment was adopted with reference to conditions existing since the foundation of our government, and the term 'involuntary servitude' was intended to cover those forms of compulsory labor akin to African slavery which, in practical operation, would tend to produce like undesirable results. It introduced no novel doctrine with respect of services always treated as exceptional, and certainly was not intended to interdict enforcement of those duties which individuals owe to the state, such as services in the army, militia, on the jury, etc. The great purpose in view was liberty under the protection of effective government, not the destruction of the latter by depriving it of essential powers.
Granted, this decision is from 1916, but it seems to take a lot for granted. The idea that conscription is an "essential power" is completely at odds with the fact that the United States has had an all-volunteer military since the 1970's and a draft has never so much as been considered necessary for the endless and innumerable military conflicts the U.S. has been involved in during that time. So the decision that the power to conscript for any reason is legally essential is, at best, no longer applicable and should be reversed.
Furthermore, this opinion completely undermines itself by stating that "involuntary servitude" "was intended to cover those forms of compulsory labor akin to African slavery," but that "it introduced no novel doctrine with respect of services always treated as exceptional." Under the Constitution prior to the Thirteenth Amendment African slavery was definitely considered "exceptional," and the idea that abolishing slavery in the United States in 1865 was not a "novel doctrine" is laughable even for 1916.
This may be an example of me quibbling over semantics, but I think that highlighting the absurdity of the language used to defend the decision also services to highlight the absurdity of the decision itself. Abolishing slavery in 1865 would likely have been considered far more extreme than abolishing any other form of involuntary servitude such as military conscription or mandatory labor, which Butler v. Perry addresses, so the idea that the Thirteenth Amendment could not possibly apply to those practices makes no logical sense.
Nobody questions that slavery was the primary target of the Thirteenth Amendment, but, despite that fact, the framers of the amendment did not see fit to explicitly abolish slavery solely in the wording of the amendment. It does, in fact, explicitly differentiate between the two: "Neither slavery NOR [emphasis mine] involuntary servitude..." The language is clear that it abolishes all slavery and involuntary servitude in the United States, and thus registration under Selective Service for a potential military draft is unconstitutional as it constitutes involuntary servitude to the U.S. government.