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We all know this already, but apophasis (from the Greek ἀπόφημι, "to say no") is a rhetorical device where the speaker introduces a subject by saying that it should not be brought up, or even denying that they are even speaking about it. It can be a way to make an ad hominem attack ("it would be unfair to dwell on my opponent's alcoholism"), to break a taboo ("only a fool would suggest that the emperor had no clothes"), or to flatter an audience by explaining something while saying there is no need to explain it (but you knew that).
In his 1657 book The Mysterie of Rhetorique Unvail'd, John Smith defines apophasis as "a kind of irony, whereby we deny that we say or doe that which we especially say or doe".
Apophasis is one of Donald Trump's favorite rhetorical devices. In 2015, when talking about rival Republican candidate Carly Fiorina, he said "I promised I would not say that she ran Hewlett-Packard into the ground, that she laid off tens of thousands of people and she got viciously fired. I said I will not say it, so I will not say it."
- Igor Bobic, 16 February 2016, "He Would Never Admit it, But This is Donald Trump's Favorite Rhetorical Device", The Huffington Post