Refuse to enlist, maybe.
Kick out, no. You can't just put 'undisclosed reasons' on a DD214. Additionally, once someone hits 6 years, they are entitled to a discharge board. Even before that, there are ways someone can fight a discharge, which means they have to know what they are fighting.
UPDATE: Wow, 5 thumbs down already. My anti-fan club is hard at work this morning.
UPDATE 2: 10! Someone has a lot of accounts now.