“If I have said 50 words in my life to John Boehner, I’d be surprised, and every one of them has consisted of pleasantries,” Mr. Cruz told reporters, noting that he had never really worked with Mr. Boehner.

And therein lies the problem. Mr. Boehner, who suffered as Mr. Cruz wooed rebellious House conservatives into a punishing government shutdown in 2013, saw Mr. Cruz as a self-aggrandizer who put himself above the institution of Congress and even the good of his party. To an institutionalist like Mr. Boehner, there is no greater offense.

Mr. Cruz, on the other hand, saw Mr. Boehner as a handy symbol of Washington deal-making and the standard-bearer for what Mr. Cruz deplores as the “Washington cartel,” a much more ominous way of describing the political establishment. It was destined to be a nonrelationship forged where Lucifer resides.

While Mr. Boehner no doubt enjoyed the attention accorded his biting remark on Mr. Cruz, it worked out for Mr. Cruz as well. He got the opportunity to again burnish his anti-Washington credentials and position himself as a warrior against Mr. Boehner and Donald J. Trump, who Mr. Boehner said in the Stanford talk was a “texting buddy.” Mr. Boehner said that they had golfed together, and that he would vote for Mr. Trump if it came to that, but not for Mr. Cruz.

To anyone who knew Mr. Boehner in Washington, the comments, first reported by The Stanford Daily, were no surprise. With a glass of wine in one hand and a cigarette in the other, Mr. Boehner would often hold forth, offering his rather spirited views of individuals and ideas, though not always for publication. And when he was in exile from the leadership from 1998 to 2006, he was a go-to quote for commentary on the poor conduct of those who were in charge.