Is the submarine service really voluntary like Dodge said?

In the early stages of the movie Dodge tells the admiral's son that the sub service is entirely voluntary and he could just quit, to which the kid says that his father, an admiral, won't let him.

Is it true that the submarine service is voluntary? I've never served so maybe I'm off base (pun not intentional, just not avoided), but given the number of submarines in the fleet I can't imagine getting enough volunteers to be in a tin can with no privacy and nothing but men around for months at a time. I know I wouldn't volunteer if I had any other alternative. And the guys they train for Morse and foreign language interception and translation, the mechanics, the electronics repairmen, would they really be allowed to say "No, I'll do it in a plane or from some radome-ridden base, but I'm not going to go in a submarine?"