In private schools, administrators must be responsive to parents because they pay the bills. Though coaches and fans feel that private schools have all the advantages -- and they do have many -- the administrative side is much different. In public schools, benign neglect is usually the case, as administrators are hugely overworked, but in the private arena, if an influential parent (a board member, say, or parent of multiple children who attend or may attend the school) has input, it will be listened to.
And the literal bottom line is this: If two or three parents are upset enough that they are willing to pull their child from the school and cost the school $50,000 for each withdrawal, that's a serious chunk of change. So would you fire an at-will employee to save $100,000? Easy call, really ...