I'm 100% sure he's not following me for a quest. I've finished all the companion quests and have killed Farkas and Vilkas numerous times. And he doesn't just follow you, he talks to you over and over and over making very difficult to play. They've stopped respawning for me but now i can't take on a new follower. I'm suspicious that a quest that automatically replaces your follower with a required follower will solve this problem, However, i can't think of any quests that do such a thing that i haven't already completed. One i know of is Proving Honor in which Farkas is your Shield Brother. Unfortunately i've completed that one already.
I am thinking the same in my similar circumstance. The missions for the companions are done, at least after the major turning point in their story arc, and when coming back to their base it asked me to check the companions for work so I did. I talked to Farkas and he wanted to see if Dragons were real and gave a location of one he knew about high in the snow mountains of the North. I took him there and got wasted several times by the Dragon so I backed off and did other quests to level up. I never could get anything out of Farkas other that training, so he kept following me making himself useful when he could. Well, I go back to that mountain and finally slayed the dragon but after I complete it, he still hangs around...only now he talked about me killing the dragon and his amazement. So we left the area and he reverted back to before, still following me and still not allowing me to dismiss him. I hate to kill the guy but I want another companion...at the least give be able to give him armor and equipment! I'll look through my quests and see if there is another I looked over that he is supposed to be attached to, but it's probably a bug.
I anyone else has seen what happened to me and got rid of him, without killing him and ruining companions following for the rest of my game, please post! Thanks!