Could be that Ainge wanted him til the trade deadline for a couple if reasons.
1. It gives the impression to other teams that there is no discord, no disfunction, no reason to think you can get one over on us. Business as usual, we are trying to improve. They were absolutely not looking to tank as some have suggested, rather they were very obviously trying to get better. You approach that in a strong unified way. Ainge has a history of playing hardball and giving another team leverage just isn't his thing, thus, your coach of 8 years is fully on board.
2. It's an obvious, if meaningless, stopping point in the season. "Stay til the deadline"