“My guess would be Alzheimer’s,” he said. Later he added, “I honestly believe he’s incapable of working another job, but that’s just my opinion.”

A doctor has never told Mr. Benjamin that he has Alzheimer’s disease, his lawyer said.

Mr. Sparks apologized for the anti-gay content of his emails in a statement on Twitter on Monday. He said the emails did not accurately portray his views on the L.G.B.T. community and were sent during a heated argument “under stressful and tumultuous conditions.”

“I believe in and unreservedly support the principle that all individuals should be free to love, marry and have children with the person they choose, regardless of gender identity or sexual orientation,” he wrote. “This is and has always been a core value of mine.”

“I am an unequivocal supporter of gay marriage, gay adoption and equal employment rights and would never want to discourage any young person or adult from embracing who they are,” he added.

The emails’ content portrayed a school grappling with other questions of diversity.

In one email, Mr. Sparks defended the school’s “lack of diversity” by saying its mostly white racial makeup had “NOTHING to do with the school or anyone at the school” and “nothing to do with racism or vestiges of Jim Crow.”

Instead, he attributed the low levels of minority enrollment to “1) Money and 2) Culture.”

But the possibility of a club for gay students appeared to be a particular problem for the school’s board. Mr. Sparks said in one email that board members and other school staff members had come to believe Mr. Benjamin was elitist and condescending, and did not respect their hard work or religious views.

“My opinion is you should have waited at least a year for these kinds of things,” Mr. Sparks wrote. “As for the ‘club,’ there obviously can’t be one now, though you might open your doors at your home if you feel qualified to talk to them about it in small group settings.”