Based on his Reserve agreement, good question. I can only surmise that he either requested to stay in the Standby Reserves or the system worked in such a way that the officer had to request to be discharged otherwise he would remain in the Standby Reserve. In my case, I don't recall ever asking to stay in the Standby Reserve or to get out. This would be a good question to ask of BUPERS or whatever they call themselves today. It wouldn't even require a SF 180.
No need to ask the Navy.
The system does work so that, once your obligated service time is served, a commissioned officer has to specifically resign his commission in order to be discharged.
If, as in your particular case, you never ask "to stay in the Standby Reserve or to get out", you then serve "at the pleasure of the President" and then stay in the Reserves until the Navy sends you your Retirement Certificate or until some Navy Board decides that the Navy can get along without you.
It is true that Kerry could have "done nothing" and thereby stayed in the Reserves until 1978. However, Kerry's Navy history shows a very sharp "sea-lawyer" that knew every angle and gamed the system to request everything he could including a release from his combat tour after only 4 months.
Unlike you and I, Kerry demonstrated an anxiousness to get out of the service as soon as possible, even to the point of allegedly "requesting a disharge" early on 3 JAN 1970.
Hey, if you are going to engage in the activities John Kerry engaged in, it would be smart to resign your commission as soon as you legally could lest the Navy recall you to active duty for UCMJ investigation of prior active duty war crimes you admitted to.
Only his signing of his Form 180 will clear up this question.
Every other Presedential candidate, including Al Gore, signed his Form 180. There is no reason not to sign it if your record is clean.