In the intense two-month tussle surrounding Harvard’s president, billionaire investor William A. Ackman positions himself as a defender of Jewish students and a champion for those critical of liberal orthodoxy on college campuses.

However, beneath the surface, Ackman’s ire is fueled by personal grievances that predate the recent campus turmoil sparked by the Oct. 7 attack by Hamas on Israel and subsequent events in Gaza. Ackman openly admits and others confirm that he harbors resentment because officials at his alma mater, Harvard, where he has generously donated tens of millions of dollars, and its president, Claudine Gay, have not taken heed of his advice on various matters.

Most recently, this involves navigating how to address complaints of antisemitism and the looming threat of violence against supporters of Israel on campus.

Expressing his perspective, Mr. Ackman shared in an interview, “It would have been smart for her to listen, or to at least pick up the phone,” recounting a recent attempt to reach out to Dr. Gay. This outreach was part of a continuous stream of calls, texts, and letters directed at university officials.

On Tuesday, Harvard’s board made a decisive announcement that Dr. Gay, the institution’s first Black president, would retain her position despite fervent calls for her removal. Although Mr. Ackman’s campaign, which included the controversial accusation that her hiring was influenced by race and gender, did not achieve its primary goal, it did leave an indelible mark.

Ackman succeeded in shaping the discourse on antisemitism within universities and underscored questions about the influence of major donors in steering the trajectory of elite institutions. Despite the contentious nature of his efforts, he maintains that he aims to be a “positive force” at the school.

Concerns over the perceived influence of a wealthy alumnus sparked a campaign supporting Dr. Gay. Despite this, Mr. Ackman retains backing from certain campus factions, notably Jewish groups critical of the university’s response to the Hamas attack and its handling of threats against Jewish students. Ackman highlighted his engagement with 230 Jewish students in a recent town hall during a campus visit.

Rabbi Hirschy Zarchi of Harvard Chabad, a host to Mr. Ackman on campus, remarked, “When the history of this moment is written, Bill will be a part of it.”

In his distinctive approach, Mr. Ackman, an active presence on social media with nearly one million followers, stands out as a rare high-profile donor publicly challenging Harvard. Unlike others, such as financier Kenneth Griffin, who express their viewpoints discreetly, Ackman positions himself as a public adversary.

Over the weekend, the University of Pennsylvania’s president, M. Elizabeth Magill, resigned amid organized resistance from influential alumni. Last week, at a congressional hearing, a controversy ensued when Ms. Magill, Dr. Gay, and Sally Kornbluth, the president of MIT, appeared to sidestep questions about whether students should face discipline for advocating the genocide of Jews.

Bill Ackman, according to Chris Rufo, a senior fellow at the conservative Manhattan Institute for Policy Research, is the catalyst behind the backlash against institutions. Rufo, known for his criticism of university diversity programs and critical race theory, lauded Ackman as an “elite defector.” This sentiment resonated with several Harvard donors who supported Ackman’s goals but hesitated to voice their approval publicly, fearing potential harm to their relationship with the school.

On the contrary, Ben Eidelson, a Harvard Law School professor, holds a different view. Eidelson characterizes Ackman as “an interloper,” arguing that the university’s functionality would be compromised if it became answerable to arbitrary wealthy individuals and the online mobs they could mobilize on platforms like Twitter.

At 57 years old, Bill Ackman boasts an estimated fortune of $3.8 billion, as reported by Forbes. Despite a history of supporting Democrats through donations, he’s best known for founding the hedge fund Pershing Square Capital. Ackman has engaged in high-profile battles against companies he deems mismanaged, including a billion-dollar bet against Herbalife, which he labeled a fraud—though the allegations were never proven. Notably, during the onset of the Covid-19 pandemic in 2020, he earned $2.6 billion by predicting a stock market downturn.

In recent years, Ackman has weighed in on diverse and contentious public issues, spanning the pandemic and Russia’s attack on Ukraine to the collapse of Silicon Valley Bank, the presidential campaign of Robert F. Kennedy Jr., and events surrounding Elon Musk. Reflecting Pershing Square’s playbook, Ackman demonstrates a commitment to exerting significant pressure to bend companies to his will.

Despite contributing tens of millions of dollars to Harvard over the years, Ackman doesn’t rank among the school’s top donors, given Harvard’s history of attracting nine-figure donations. His most substantial contribution dates back to 2014 when he and his then-wife announced a $25 million donation to expand the economics department and establish three endowed professorships.

Recently, he made a smaller donation to the rowing crew, a team he was part of during his undergraduate years.

However, insights from interviews with him and 10 associates unveil a slow deterioration of the relationship with his alma mater.

During a Monday interview, Mr. Ackman recounted an incident just over a year ago when Dr. Gay, then the dean of Harvard’s Faculty of Arts and Sciences, visited his waterfront Manhattan office. Their conversation covered various topics, including Ackman’s intentions to contribute more funds to the institution.

It happened roughly two months ago, and the memory of that forty-five-minute conversation still lingers as a pleasant one, giving him hope that she might be receptive to his suggestions. Following the tragic assault in Israel on October 7, he used that recent call to express concerns about the safety of Jewish students and his dissatisfaction with the university’s official response. Dr. Gay passed on his message to Penny Pritzker, the chair of Harvard’s governing board, sparking what Ackman described as “an entirely disappointing conversation.” Unfortunately, Ms. Pritzker chose not to respond to messages seeking comments.

People who have discussed the matter with Ackman reveal that, for at least the last three years, Harvard has been a source of private frustration. This frustration partly stems from the university’s leadership dismissing his recommendations regarding the establishment of a testing facility to facilitate the return of staff and students to campus during the pandemic.

In an event not previously reported, two years ago, Ackman cautioned members of Harvard’s fundraising team that if they didn’t heed his advice on investing an earlier donation, he might withhold future contributions. According to two individuals familiar with the conversations, Ackman conveyed his concerns about the financial acumen of Harvard’s administration through a series of strongly worded letters. Despite the conflict, he ultimately decided to increase his donation.

When asked about that incident, Mr. Ackman brushed it off as “a distraction from other things” and chose not to delve into further details. Harvard’s spokesperson, similarly, declined to provide any commentary on the school’s interactions with Mr. Ackman.

Drawing parallels, Ackman likened Harvard’s lack of engagement with him to the early days of his career as an activist investor, where he faced unreturned calls from chief executives of targeted companies. However, he noted that the current trend is for corporate boards to invite him in for discussions.

On November 4, he penned a four-page letter to Dr. Gay, articulating his concerns about antisemitism on campus and what he perceived as double standards for different racial and ethnic groups. In this detailed letter, he outlined specific actions he wished the university to undertake.

Following the letter, Ackman claimed to have minimal contact with Harvard. Nonetheless, he continued to raise questions about Dr. Gay on social media and in public forums, going so far as to promote claims that she had plagiarized academic research.

In response, Harvard’s board stated that Dr. Gay had not violated the school’s standards for research misconduct. Still, they acknowledged that she would retroactively incorporate additional citations and quotations into earlier research.

Marc Rowan, a private-equity mogul heading the board of advisers at the University of Pennsylvania’s Wharton School, recently conveyed to associates that he was stepping back from publicly advocating for the removal of the university’s president. This shift in approach was due to concerns about potential harm associated with linking the effort to a wealthy Wall Street investor, as reported by people familiar with the conversations.

Mr. Ackman, who has been facing criticism for attempting to identify students in groups attributing blame to Israel for the Hamas attack, remains undeterred by detractors. He brushed off concerns, stating, “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.’” Notably, he claimed to have received calls from some of the world’s most prominent figures expressing a wish to articulate similar views. Even among Mr. Ackman’s supporters, some expressed a wish that he had followed a similar course, albeit anonymously, fearing they might become targets themselves. Mr. Ackman, however, asserted that a more reserved approach wasn’t viable, given his lack of a formal role on any Harvard boards. “They didn’t let me in,” he emphasized.

Expressing his commitment to sharing concerns with Harvard’s administration, Ackman also predicted that others would delve into Dr. Gay’s academic record. On Monday, he asserted, “I don’t see a scenario where she survives for the long term or intermediate term.” However, he refrained from commenting on Tuesday’s news that Dr. Gay would retain her job.