4. Seattle Seahawks
Pete Carroll decided on not going with Matt Flynn after they brought him over from Green Bay and went with Russell Wilson, which lead to an 11-5 season and won a playoff game on the road. That lead to Seattle trading Flynn to the Oakland Raiders in favor of Wilson being the future. Now Tebow wouldn't be the starter over Wilson, but as a backup? Carroll didn't think so, which is why they signed Brady Quinn. From the Seattle Times:
The use of the option running game is also a reason many thought Seattle might look to bring in Tebow, the former first-round pick who played for the Jets last year after being acquired from Denver. While not a strong passer, Tebow is an effective runner as a quarterback and led the Broncos to a playoff victory two seasons ago. Tebow remains with the Jets and is set to make more than $2 million. While the Seahawks did look into acquiring him, he's not thought to be a consideration.
Behind Wilson, Tebow could have been a nice fit in Seattle, but Carroll saw differently.