He wants to win. He knows how to build a system to win. Staff and front office said they would provide him with that skillset given past success. He is stuck with players that can't or won't play the system needed to win and he is losing it in real time.
He is looking at a roster that is a hodge-podge of skills that don't fit together outside of lines 1 and 4. If he tinkers breaking up line 1 they could likely nosedive until they find where March and Pasta fit when not aside Bergeron. That's taking them out of playoff contention. If he doesn't, they are falling out of playoff contention. Lose - lose. If you are giving up family, friends, and working 80+ a week and see this it eventually burns you up in any role, irrespective of the checks you're taking home.
At this point it's up to the players to play better and play the roles they are being asked to play. That includes March and Bergeron getting guys in line, not just by lead by example or chirping, but in different ways as leaders. It's partially on them as well as vets and leaders on the roster.
Even though Butch can be a bit of a prick at times, I do feel for the guy as you can see it's burning him up. To use an analogy, he's being told to run a Michelin restaurant and go for another star, while his GM is giving him stale bread and smelly fish to go along with a few prime grade ingredients. It doesn't work that way to deliver on excellence and I see this really being on the front office and players at this point.
He will likely get the gate first because that's just how it goes, but I don't see it being on him. He really knows the game and has grown a lot as a coach since the Washington days and will have another job if he wants to give it another go somewhere else.
PS: Getting back to the player thing, WTF happened to not re-up Markus J given the synergy with Coyle after that run? As a GM you see that magic and you put it in a bottle as long as you can. They had it in their laps and let it go and have tried for 2 years to rekindle that with others and none have worked. That's just one of the things that makes you go wtf in the night with the front office and another example of not being decisive on what skill and style they want to build to.