Doesn't say when Melo gave the ultimatum. When it must have been obvious MDA was not returning it made no sense for him to stay.
Coaches used the end of a season to evaluate and perhaps experiment. When it was known Woodson was to be the next guy, it makes no sense to humiliate MDA and fire him, so let him move on, let woodson perhaps end the season with continuity and all go on.
The ultimatum could have been there and not a "Flash point" to where MDA just ups and quits.
MDA was not the guy for that roster and it was apparent when they traded the house for Melo that MDA never had leverage. If and When Melo was not buying into MDA, it was problem. Expiring coach and a younger melo was the right choice for knicks at the time.
Currently, 33 year old Melo with two years left does not have that leverage anymore nor the time frame to build with or around him. He can still play but he is not changing his spots, stripes or his game.