The mistake was not trading Hayward for some kind of value at the deadline last season.
If the team had reason to think Hayward was going to opt out and get a good offer, they should have traded him.
If the team was completely surprised by Hayward's decision and/or the fact that other teams were willing to offer more, then that was a failure of a different sort.
Hindsight is 20/20 obviously ... this would look different if Hayward had been healthy for the playoff run and the Celtics had made the Finals because of his strong play, for example. In that case you might say well, it was worth holding on to him despite the risk of losing him because the Celts made a Finals run.
Then again, Hayward was injured for most of the important games that happened during his time under contract with the Celtics. So you could argue it was foolish to expect him to contribute to a deep playoff run.
Anytime we second guess the coach or management, it's important to keep in mind that we don't know what they did or did not know or when they knew it. We don't know what they tried to do or what any of the people involved said.
Still, between Kyrie, Horford, and Hayward it seems like you have three guys that the team at least had some thought might want to stick around at a price the team would be willing to pay, and in each instance that turned out not to be true. I don't buy that there's something "wrong" with the Celtics organization that caused those players to want to leave.
I do wonder if there's something wrong with the organization insofar as gathering internal intelligence on their own players to have some idea of what the players are going to do when they hit free agency.