Mr. Trump brought up Mr. McCabe’s wife on several occasions, including a face-to-face meeting in which the president called her a “loser.”

Does Mr. Trump’s criticism have merit?

Yes and no. Mr. McCabe did not begin supervising the Clinton investigation until after his wife had lost the race, and records show that he sought ethics and legal advice inside the F.B.I. before deciding not to recuse himself. But some in the F.B.I. believe he should never have been involved because of his wife’s campaign donations.

When he ultimately recused himself, late in the investigation, it only fueled the argument that he should have stepped aside from the beginning.

Mr. Trump’s theory of Mr. McCabe as a pro-Clinton partisan, however, is on far shakier ground. Mr. McCabe has identified himself as a lifelong Republican and did not vote in the 2016 election. The newspaper story that Mr. McCabe authorized F.B.I. officials speak about was not a positive one for Mrs. Clinton.

And, perhaps most importantly, in the months before the election, when the F.B.I. publicly disclosed information about its work on the Clinton investigation, it never revealed the existence and scope of a full-throated investigation into the Trump campaign’s Russia ties.

What does this possibly have to do with Russia?

Like so much at the F.B.I., Mr. McCabe’s firing has become inextricably entangled in presidential politics and the investigation by the special counsel, Robert S. Mueller III.

Mr. McCabe was one of only a handful of F.B.I. officials involved in the Russia investigation from the first days. He supervised it at every step and was involved in the decision to seek a wiretap on Carter Page, a former Trump foreign adviser. That wiretap application was approved by senior Justice Department officials, was reapproved by Mr. Trump’s own Justice Department and was signed by a federal judge based on evidence that Mr. Page was a Russian agent. Mr. Trump has declared that wiretap to be improper, however, and points to it as evidence of political surveillance by the F.B.I.