In the two-month battle over the fate of Harvard’s president, the billionaire investor William A. Ackman has cast himself as a protector of Jewish students and the standard-bearer for people who believe colleges have fostered a hostile atmosphere for critics of liberal orthodoxy.

But behind his anger are personal grievances that predate the uproar that has engulfed campuses since the Oct. 7 attack by Hamas on Israel and Israel’s subsequent invasion of Gaza. Mr. Ackman, by his own admission and according to others around him, resents that officials at his alma mater, to which he’s donated tens of millions of dollars, and its president, Claudine Gay, have not heeded his advice on a variety of topics.

Most recently, this includes how to respond to complaints of antisemitism and the specter of violence against supporters of Israel on campus.

“It would have been smart for her to listen, or to at least pick up the phone,” Mr. Ackman said in an interview, describing a recent outreach to Dr. Gay that was part of a stream of calls, texts and letters to university officials.

On Tuesday, Harvard’s board announced that Dr. Gay, its first Black president, would stay in her post despite calls for her removal. Though Mr. Ackman’s campaign — which has included the accusation that she was hired in part because of her race and gender — failed to unseat her, he succeeded in shaping the debate about antisemitism at universities and showcasing questions about the power of major donors to dictate the direction of elite institutions. He said he wants to be a “positive force” at the school.

Those sensitive to the perception that a wealthy alumnus could exert such influence over the school mounted a campaign to back Dr. Gay. Mr. Ackman maintains support from some corners of campus, including Jewish groups who feel that the university was too slow to forcefully condemn the Hamas attack and has since equivocated on threatened violence against Jewish students. Mr. Ackman noted that he met with 230 Jewish students in a town hall on a recent trip to campus.

“When the history of this moment is written, Bill will be a part of it,” said Rabbi Hirschy Zarchi of Harvard Chabad, who also hosted Mr. Ackman on campus.

Mr. Ackman, who posts frequently on social media to nearly one million followers, stands virtually alone among high-profile donors to Harvard in making himself a public adversary of the school. Other wealthy Harvard donors like the financier Kenneth Griffin have pressed their perspectives only behind the scenes.

The president of the University of Pennsylvania, M. Elizabeth Magill, resigned this weekend amid organized pushback from high-profile alumni of the school. Ms. Magill, Dr. Gay and Sally Kornbluth, president of the Massachusetts Institute of Technology, set off a furor at a congressional hearing last week, when they seemed to evade questions about whether students should be disciplined if they called for the genocide of Jews.

“I don’t think we would have seen anything nearing the level of backlash against these institutions had it not been for Bill Ackman,” said Chris Rufo, senior fellow of the conservative Manhattan Institute for Policy Research, an outspoken critic of university diversity programs and topics like critical race theory. Mr. Rufo praised the hedge fund manager as an “elite defector,” a sentiment shared by a half-dozen Harvard donors who said they supported Mr. Ackman’s aims but were reticent to speak publicly and damage their relationship with the school.

There are others who disagree. Ben Eidelson, a professor at Harvard Law School, described Mr. Ackman as “an interloper.” “We can’t function as a university if we’re answerable to random rich guys and the mobs they mobilize on Twitter,” he said.

Mr. Ackman, 57, has an estimated fortune of $3.8 billion, according to Forbes, and a history of donating to Democrats. He founded the hedge fund Pershing Square Capital and for years waged high-profile, drawn-out battles against companies he believes to be mismanaged. He lost a billion-dollar bet against the nutritional food supplement company Herbalife, which he called an outright fraud — allegations that were never proven. At the start of the Covid-19 pandemic in 2020, he made $2.6 billion wagering that the stock market would drop.

In recent years, Mr. Ackman has also frequently weighed in on hot-button public issues, including the pandemic, Russia’s attack on Ukraine, the cryptocurrency exchange FTX, the collapse of Silicon Valley Bank, the presidential campaign of Robert F. Kennedy Jr. and the various goings-on around Elon Musk.

Key to Pershing Square’s playbook, which Mr. Ackman seems to have adopted in his battle against Harvard, is a commitment to go to great lengths to pressure companies to bend to his will.

He has given tens of millions of dollars over the years to Harvard, but does not rank among the top donors at a school that has landed numerous nine-figure donations. His largest gift dates to 2014, when he and his former wife announced a $25 million donation to expand the economics department and endow three professorships.

More recently, he gave a smaller sum to the rowing crew, a team he joined as an undergraduate.

But interviews with him and 10 associates revealed a gradual degradation of the relationship with his alma mater.

In the interview on Monday, Mr. Ackman recalled that a little over a year ago, Dr. Gay, who at the time was dean of Harvard’s Faculty of Arts and Sciences, paid a visit to his waterfront Manhattan office. The topics of discussion included Mr. Ackman’s plans to donate more money.

The 45-minute chat was pleasant, he recalled, and so he expected that she might be receptive to his input roughly two months ago, when he called her to discuss his concerns about the danger to Jewish students after the deadly Oct. 7 attack in Israel, and his disappointment in the university’s official response to it.

Dr. Gay forwarded his message to Penny Pritzker, leader of Harvard’s governing board, who engaged Mr. Ackman in what he described as “an entirely disappointing conversation.” Ms. Pritzker did not respond to requests for comment.

Mr. Ackman has privately steamed at Harvard over at least the past three years, several people who have discussed the subject with him say, in part after the university’s administration brushed off his suggestions for how to set up a testing lab to get students and staff back to campus during the pandemic.

Two years ago, in an incident not previously reported, Mr. Ackman told members of Harvard’s fund-raising team he might not give another dime because they hadn’t heeded his advice on how to invest an earlier donation, said two people with knowledge of the exchanges. Mr. Ackman sent off a series of fiery letters to Harvard administrators questioning their financial acumen. He wound up donating more money anyway.

Asked about that episode, Mr. Ackman said it was “a distraction from other things” and declined to answer questions about it. A Harvard spokesman declined to comment on school’s interactions with Mr. Ackman.

Mr. Ackman compared the university’s lack of engagement with him to companies he targeted in his early days as an activist investor pushing for changes. Then, he would call chief executives and wouldn’t get his calls returned. Now, he said, it’s more common for corporate boards to invite him in.

On Nov. 4, he wrote a four-page letter to Dr. Gay, outlining his concerns about antisemitism on campus and what he called double standards on campus for different racial and ethnic groups. He offered a detailed list of actions he wanted the university to take.

After sending that letter, he said he had minimal contact with Harvard. He continued to raise questions about Dr. Gay on social media and in public forums, including by promoting claims that Dr. Gay had plagiarized academic research.

Harvard’s board said that Dr. Gay had not violated the school’s standards for research misconduct, but that she would retroactively add additional citations and quotations to earlier research.

Another billionaire financier agitating for change at an elite university, the private-equity mogul Marc Rowan, tried a different tack. Mr. Rowan, who headed the board of advisers at the University of Pennsylvania’s Wharton School, had been publicly calling for the ouster of the university’s president, but last week told associates that he was stepping back, worried it could do more harm than good to associate the effort with a wealthy Wall Street investor, people briefed on the conversations said.

Even some of Mr. Ackman’s supporters said in interviews that they wished he had heeded the same advice, though they didn’t want to be named for fear of becoming Mr. Ackman’s target themselves. Mr. Ackman said that a more demure approach wasn’t an option, as he had no formal role on any Harvard boards. “They didn’t let me in,” he said.

Mr. Ackman, who was criticized after he sought to identify students in groups that blamed Israel for the Hamas attack, said he doesn’t give much thought to his detractors.

“For every email I’ve gotten saying, ‘You’re a racist.’ I’ve gotten 1,000 people saying, ‘What you’re saying is what I believe’,” he said. “I’ve gotten calls from some of the most prominent people in the world who said, ‘I wish I could say what you’re saying.’”

He said he will continue to share his concerns with Harvard’s administration and others at the school. He also predicted that others would continue to mine Dr. Gay’s academic record. “I don’t see a scenario where she survives for the long term or intermediate term,” he said on Monday.

He declined to comment Tuesday on the news that Dr. Gay would keep her job.