The same two reasons why anything is what it is in this world: money and power.
Part II of the national media reaction to the notice of allegations from the NCAA regarding UNC's football team is "how can UNC justify having Butch Davis remain as head football coach?" The answer is simple: nowhere in the entire 42-page NOA is Butch Davis' name mentioned, so other than being at the helm while the Titanic hit the iceberg, he escapes culpability.
That then raises the question of "isn't that enough", and from a contractual standpoint, it is probably not. Davis is under contract to be UNC's football coach through the 2014 season. His contract does provide for termination with cause under the following provisions:
a violation by COACH, or knowing participation in a violation by COACH, or a violation by the assistant coaches under COACH'S supervision of which COACH had reason to know, should have known through the exercise of reasonable diligence in the exercise of his duties under this Agreement, or which COACH condoned, of a major NCAA regulation or bylaw, or of a major ACC regulation or bylaw, or of a policy of or applicable to UNIVERSITY...
a violation by Football Program staff members (other than assistant coaches) or by student-athletes under COACH'S supervision, of which COACH had reason to know or which COACH condoned, of a major NCAA regulation or bylaw, or of a major ACC regulation or bylaw, or of a policy of or applicable to UNIVERSITY...
On the surface, it seems like a slam dunk that UNC would be well within its rights to fire Davis under those clauses. The only problem is that UNC is mounting the "rogue tutor", "rogue player", and "rogue coach" defenses to the NCAA, positions supported by the absence of any mention of Davis in the NOA. UNC can't claim Davis didn't know anything to the NCAA then turn around and fire him with cause because these things happened on his watch.
That means if UNC wanted to fire Davis just to wash their hands of him, they would have to pay. Davis' contract calls for a buyout equal to $275K plus the base salary for each season left (4 times $315K) plus deferred and other compensation. That's $1.5 million base dollars before you start getting into the millions in deferred compensation he would be owed. I'm sure an exit would be negotiated, but the starting point of a buyout would probably be in the $2-2.5 million range. That's mighty pricey for a program in the middle of a $70 million stadium expansion, even for a school with deep pockets like UNC.
The other factor keeping Butch in place is his support among the powers that be at UNC, and I don't mean simply Holden Thorp and Dick Baddour. People have wondered how Thorp and Baddour could so openly support Davis, and the answer lies in the fact that much of Davis' true support lies above their pay grade. UNC insiders have said that the seat of that support is in UNC Board of Trustees chairman Bob Winston, who is rumored to have engineered the selection of Davis as football coach in 2006.
Similarly, despite the NCAA unpleasantness, Davis appears to continue to have the support of big money donors, many of whom would be asked to step up if Davis had to be bought out. This is not to say that there are some big-timers who are disgusted with him and the whole football mess, and some of them have withdrawn their support of the Blue Zone project. But he fact that Davis was not directly implicated in the NCAA allegations does not seem to have moved the needle much in either direction in regards to Butch's standing with the powers that be. Those who didn't like him still don't, and those that support him still do.
(It is important to note here that I am basing the last paragraph on anecdotal evidence and not anything concrete - just a sense of the meeting, as the Quakers say)
So in the absence of any truly actionable offenses by Davis that would trigger his immediate dismissal and any groundswell of dissatisfaction among those who make the decisions and pay the bills, Davis remains almost by default. Even if Holden Thorp and Dick Baddour hate Davis as much as the NCAA hates Chris Hawkins and want to fire him every day, without those two things, there's not much they can do. And if Davis is going to have to stay, then at least publicly they will offer support.
There is still a long way to go before this thing is finally put to rest, however. The penalty phase is yet to come, and in a sense the allegations remain surreal until there is an actual price to pay. In addition, UNC football will be under intense scrutiny both on and off the field this season, and Davis' reservoir of good will is long since dried up and his margin of error is nil. If Davis continues to play the role of Captain Hazelwood while the Exxon Valdez runs aground again either on or off the field, this situation could change rapidly.