I know it’s popular to say it’s quarterback, but it’s not.
Adam Gretz, in light of Mike Richard’s firing by the Columbus Blue Jackets, does a great job breaking down the number one reason coaches get fired, bad goaltending. He even links to a story about how often Jack Adams award winners have the opposite situation, good goaltending, and points out the number of coaches on both lists!
It’s not a coincidence.
You cannot overcome bad play from a goaltender in the NHL. There may have been a time when you could go out and outscore teams, winning games 5-4, 6-5, etc, on a regular basis, but those days are long gone. You simply cannot win when you’re giving up 3-4 goals every game, and coaches that don’t win consistently get fired.
So, you want to coach in the NHL? you’re livelihood will be dependent on some of the quirkiest athletes on Earth. Good luck with that!