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There it was for all to see, President Trump’s tangled relationship with the Ivy League, delivered in a burst at his rally in Michigan on Tuesday night.

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“He’s the top,” the president said of Dr. Mehmet Oz, the TV celebrity doctor he chose to oversee Medicare and Medicaid. “I mean, he went to Harvard.” But then: “I shouldn’t even mention that anymore because that used to be a good thing. Today it doesn’t mean much.”

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There was this about Gen. Mark A. Milley, the president’s first-term choice as chairman of the Joint Chiefs of Staff: “You know, he went to Princeton,” Mr. Trump said in 2019. “And he went to Columbia.” But then: “I’m not sure, was that a good thing or a bad? Did I like it or not?” The president never answered, although he called General Milley, whom he has since reviled, a “smart cookie.”

And on Justice Brett Kavanaugh: “He was, I believe, No. 1 at Yale,” Mr. Trump said in 2018 of his Supreme Court nominee. “Is that a correct statement?” It was not, since Yale does not calculate class rank.

What is correct is that the president’s war on academia has focused intensely on the Ivy League, the richly endowed collection of eight schools, most founded in the colonial era, that cost $90,000 or more a year, send a disproportionate number of graduates into America’s leadership class and accounted for less than 1 percent of the nation’s undergraduate enrollment in the fall of 2022.

Mr. Trump’s attacks on this elite group — Harvard, Yale, Princeton, Columbia, Cornell, Brown, Dartmouth and the University of Pennsylvania — have endeared him to his political base. He is withholding, or threatening to withhold, billions of dollars in federal funding from six of the eight schools because, he says, they are citadels of antisemitism and liberal indoctrination. Officials in higher education acknowledge failures, but call the president’s crackdown a perilous threat to academic freedom.

The Trump administration has targeted many other colleges and universities for potential antisemitism, some 60 in all. And yet the eight Ivies are cultural touchstones for Mr. Trump. Beyond the politics is a complex brew of resentment and reverence that the president, an Ivy League graduate himself, has long harbored for a club that has never really accepted him.

“They don’t return the love to him,” said Alan Marcus, a business and political consultant who oversaw Mr. Trump’s public relations from 1994 to 2000. After the president’s companies went through multiple bankruptcies in the 1990s, Mr. Marcus said that as part of an attempted comeback for his client he tried to get Mr. Trump to deliver a college commencement address or receive an honorary degree.