Reportedly, Kane wanted to go to a team he thought he could win with. He also wanted term and he wanted to play a prominent role on his new team. So far the Red Wings look like they can compete this year although they do not have a recent track record of playoff success so that is yet to be seen. His role on the team is also yet to be seen as he has not played a game yet. One thing we know for sure though, is that he did sign a one-year deal, so clearly, term was not that important to Kane.
The fact that Kane was willing to turn down term is significant given the nature of his offseason hip resurfacing surgery. No player to return from the procedure has ever lasted more than one season after having the surgery so the fact that Kane was willing to turn down job security means that he is confident in his health.