Briggs made a comment in preseason that not everyone had bought in yet. After the season it was speculated that he was referring to Peppers.
I've seen many times in the corporate world where a new management team comes in and some of the existing employees (particularly really talented people) tend to groan and whine about all the changes. Their points usually tend to fall along the lines of "We've done this such and such a way for years and we've always performed at a high level." I've seen those types stay, I've seen them leave voluntarily, and I've seen them fired. The ones that stay tend to be miserable. The ones that leave end up better off because they find a new situation that they accept at face value because it's new.
Now in this instance, I have to imagine that Urlacher (who was very close to Lovie) might not be thrilled with ANYTHING that changed. And, being a leader, he could have had a negative influence on the younger guys simply by example. Now I for one would like to think that when games that count started, Urlacher's competitive spirit would take over and he would play at a high level. I'm just not sure that that fact alone could overcome the negatives that he might have displayed during TC that might have delayed the younger guys buying in and become a general distraction.
Personally, I was relieved when Urlacher wasn't re-signed - and in particular retired. I potentially saw a power struggle just because - well - Urlacher is kind of a vengeful dick.
As for why no other teams signed him, I think he still had enough in the tank to help some other team - and certainly the Bears if Lovie was still around. The problem may have come in where his accustomed position of leadership couldn't be given to a guy that might not even start, or would be a one year mercenary. And another concern would also have to be how much effort he would put into learning a new scheme if he was on a one year deal.
An example that comes to mind is Kreutz. He was THE leader on the offensive line for years. The Bears offered him less than he thought he was worth so he took a one year deal with the Saints for less than the Bears were offering. In October of that year, he quit the team. He just left the team because he wasn't feeling a love for the game any longer. Can anyone say bad signing by the Saints?
I'm not saying that would have happened with Urlacher either with the Bears under a new regime or with a new team, but there does seem to be the possibility that his pride may have gotten in the way and prevented him from being what he used to be on the field no matter who he may have played for.