If I remember right, they were not drafting young men over the age of 25 which is about the age Dick Cheney was during the major call up for Vietnam. I believe he was married with children, and unless you were already in the service at that age, you weren't going to be going to war.
It is typical of those who never liked Bush or Cheney to diss them for 'avoiding' military service. In Bush's case he did serve as a pilot though never in combat, as did many others. In Cheney's case, it was a matter of timing.
Class I-S: Student deferred by law until graduation from high school or attainment of age of 20, or until end of his academic year at a college or university.
Class II-S: Student deferment.
Class III-A: Extreme hardship deferment, or registrant with a child.
If he had done this, he would have been able to defend the Reagan "Don't Belong, Don't Join" policy...and I as a commander would not have had to deal with "Don't Ask, Don't Tell". I am sure James Webb would have been able to explain to Barney Frank precisely why the romantic element does not belong on the combat team. Having never commanded (in combat or otherwise), ole Dick did not and does not have a clue.
Finally, if you need a subject matter expert, you bet it is better to have somebody who has done it before. That's true of accountants, carpenters, doctors, welders, lawyers, farmers, mariners...and people who wage war! We have had eight years of folks without a clue...enough is enough.