“I gave her my vote of confidence at her election, and worked diligently to support both her presidency and the mission of the institution,” Dragas told me by phone in late August. “There just came a time when the two objectives seemed contradictory, and I acted in the best interests of the students.” Sharp-featured and intense, Dragas holds a bachelor’s degree and an M.B.A. from UVA. Her own business experience is in the Virginia Beach real estate firm founded by her father, George, a hard-driving child of Greek immigrants. By all accounts, Dragas inherited much from her father, who himself headed the board of a university, Old Dominion, some two decades earlier. “If a president can’t do it,” he once said, “we either have to work with him — or replace him.”

Helen Dragas saw her father put that blunt philosophy to work, when he hired James Koch as Old Dominion’s president. “I followed an individual who was fired using very much the same model that occurred at UVA,” Koch, who is now retired, told me. Koch went on to a successful tenure, becoming a national authority on presidential leadership, and he says he discussed the dispute over Sullivan’s resignation with several UVA board members, including Dragas. “They looked around and they said, ‘There’s a revolution going on in higher education,’ ” Koch says. “They thought that the people in Charlottesville were not responding.”

What had the board so worried? In late May, as she prepared to remove Sullivan, Dragas e-mailed a board colleague a link to a Wall Street Journal column, beneath the subject line: “Why we can’t afford to wait.” The article described a joint venture that offers free, open online courses. In the last year, Harvard, Stanford, M.I.T. and other elite schools have moved aggressively into this arena, drawing significant global audiences, if no actual revenue. While many veteran professors roll their eyes at predictions that online learning will transform the structure of universities, to certain segments of the donor community — the Wall Street and Aspen Institute types — higher education looks like another hidebound industry awaiting creative destruction. “If you’re not talking about it,” says Jeffrey Walker, a UVA fund-raiser and a former JPMorgan financier, “what’s wrong with you?”

This discussion has been influenced by the ideas of Clayton M. Christensen, a Harvard Business School professor and guru of “disruptive innovation,” the concept that established companies are often overtaken by upstart competitors because they are incapable of embracing new technologies. In his book “The Innovative University,” Christensen argues that higher education could go the way of America’s steel industry. Dragas told me she found Christensen’s ideas extremely compelling.

“Higher education is one of the last sectors of the economy to undergo this kind of systemic restructuring,” Dragas says. She and other board members emphasized, however, that online education was merely a proxy for a deeper concern about the pace of change in higher education. Dragas was equally worried about the hospital, which was competing for market share and facing changes in financing, and a decline in federal research funding. Some board members wanted Sullivan to reallocate resources from marginal to core needs, and while they weren’t sure how to achieve that shift, they wanted to hear exciting ideas from the president. Sullivan didn’t seem to be willing — or perhaps able — to provide them. Sullivan contends she was given contradictory instructions by Wynne, the rector who hired her, and later by Dragas. Was she supposed to be implementing the many plans the university had devised over the years, or coming up with new ones? Sullivan worked to strengthen her strategic thinking with a pair of business professors, but her dutiful efforts left some board members unimpressed. “She seemed, in a word, plodding,” R. J. Kirk, a pharmaceutical billionaire and board member, told me.

Some of Sullivan’s allies suggest, discreetly, that she didn’t fit the board’s image of a chief executive. She is in her 60s and has the fashion sense of an academic. In a personnel review process last year, Dragas, who is immaculately tailored, told Sullivan that she received comments from several board colleagues, questioning whether her wardrobe was occasionally too informal.

“I don’t know what the unprofessional dress was,” Sullivan said. “I do live here at the university, so when I’m working out or doing something else here, people will see me.” It’s hard to imagine anyone leveling such criticism at, say, the famously rumpled former Harvard president Larry Summers. “People are very much aware that I’m the first woman president of Virginia,” she said. “It would be naïve to think it’s not there as an issue.” Dragas calls the suggestion that she judged Sullivan by her appearance “ridiculous,” adding, “If the president had been a man, I would have conveyed the same sentiments from the board, no question about it.”