Drafting or conscription is a term used to describe where citizens of the United States are forced to fight in a war. For the most part, many people who join the military do so voluntarily. Drafting started in 1940 and continued until 1973. Many people were against the Vietnam War and at the time at the beginning of the war, men ages 18-25 had to register with the Selective Service who was responsible for holding the draft.
Not everyone was called to fight, but usually those who were in that age range and not in college would take the chance of getting called to duty. Richard Nixon who was the president in 1968 wanted to end the draft. He preferred to have an army based on volunteers.