Man management is part of it. There also needs to be a degree of technical/strategic thinking and the ability to teach/train those strategies to the players. Bellamy and Bennett have a good mix of the two. Some coaches, like Matt Elliott and Jason Taylor, have unparalleled knowledge of the game but struggle to manage a group of men, making them fail as head coaches but shine as assistants (I wonder if Price falls into this category). Guys like Robinson seem to be brilliant man managers but requires strong assistance in order to excel (Taylor, Green, Fitzgibbon etc as assistants).
Mary seems to be well liked, but completely fails in the technical/strategic section. Problem is, he isn't willing to take on help from those who can actually offer it. He even turned to the players for advice this year, which worked wonders for half a season but he has no plan b and fell back into his old ways.
As for the coach vs players thing, I always compare it to a tradie and tools. No matter how good the tradie is, he needs a set of tools to carry out a task. However, the better tradie knows how to get the job done with any set of tools, while a poor tradie will struggle no matter how fancy or expensive a set of tools he has.
Then of course, there are the moron tradies who pick the wrong tools for the wrong task and fall back on old, broken tools that fail him time and time again while completely ignoring the shiny new tools (until some other tradie grabs said new tools and uses them to win a contract). Then they'd get arrested for driving drunk to site. But y'know, they've built a shack out the back of West Wollongong, so the bosses won't get rid of him...