With Mike D'Antoni still coaching the New York Knicks, they still employ a run-and-gun style of offense that requires the Knicks to push the ball and have solid ball movement. This was seen before the trade, as Raymond Felton would push and either find Amar'e Stoudemire for a dunk, find Gallinari or Chandler on the perimeter, or find Amar'e down low, who would kick the ball back out upon a double-team.
Unfortunately, this is not the type of style Carmelo likes to play.
Carmelo Anthony needs the ball on every possession. He would prefer to slow the pace down and work strictly on isolation plays. He's a good isolation player, but he can tend to freeze others out with his style of play and is not as good of a passer out of the double-team as Amar'e Stoudemire showed he was before the trade.