You need to actually join a side in order to do this quest. Finish one of the two "join faction" quests to the point where the other one fails and you swear the oath. Then continue seasons unending.
I strongly recommend you don't though, it is absolutely atrocious and made me rage quit skyrim for a year or so. When I returned to skyrim I avoided this quest by joining a side and winning. You are also missing out on a bunch of achievements and a lot of interesting missions by not doing the civil war properly.
If you do choose to proceed with this quest, consult this section
which lists the various quests and achievements that can be broken by this quest, and how to avoid these problems.