While watching this first season, with its intricate structures of loyalties, a theory about Jack’s motivations hit me. Vaughn, Sydney, and most of the younger agents tend to speak of fighting for one’s country. When thinking about why Jack fights, that motive doesn’t seem to fit with what he says and what his position is. As a double agent, he has long ago forced half his mind to work against the very country he swore to serve. So, while he still protects America, I don’t think he really has that at heart anymore. I think that the confusion and pain caused by betrayals, loyalty shifts, and the constant fear of being a double agent have caused him to fall onto the one clear thing he can love, protect, and fight for with all his (considerable) heart: his daughter. Time after time, Jack must choose between the safe, rational, patriotic choice, and the safety and happiness of his daughter – and he always chooses the same thing, even if it means working with the enemy.
I don’t know if that makes any sense, but I like it.
Postscript about Irina: I think that though Jack both loves Irina and hates her, he never trusts her, and thus his feelings about her don't provide too much of a driving influence. Then again, I've not seen most of season two yet. However, I think his love for Sydney is the overriding passion in his life.