There is quite literally no right more fundamental than the right to do what you want to do with your own body, to the extent that it doesn't infringe on other people.

Suicide. Prostitution. Drug Use. Organ Sales.

Presently, in the United States of America, these are not choices you are legally able to make. Combine that with the idea of the draft, which puts your body at the service of the government, and I'm not certain that particular premise is actually a "right."