Rhetorical Device: Antanagoge
Antanagoge consists of presenting the audience with a negative and then putting a positive next to it. The device allows the speaker to acknowledge the negative while diminishing its relative significance. There are a number of use cases for antanagoge. One is to put a positive spin on a negative situation:
When life gives you lemons, make limonade
Antanagoge is also a go-to technique for anyone who needs to soften the blow when delivering constructive criticism. The 'point for improvement' would be 'sandwiched' between two positive comments to help make it more palatable. This is very familiar to anyone who has been to a Toastmasters club. A typical (condensed) example would go like this:
John, I loved how you grabbed the attention of the audience with that intriguing opening question. I did observe that the speech covered perhaps too many points, which makes it hard for the audience to absorb your key messages. That said, I loved how you used body language and moved deliberately around the speaking area throughout your speech. I look forward to your next speech.
Antanagoge is also a useful technique for sales, especially in objection handling:
Yes, the product is expensive but you are paying for quality which means won't have to worry about lost productivity due to break-downs.
Some sources describe antanagoge as including a situation where a person offsets an accusation by making a countercharge against the opponent. To me, this seems more like offsetting a negative with another negative (rather than with a positive), so I view it as not truly being an example of antanagoge, but rather one of the figures of refutation described on the authorative Silva Rhetoricæ website (such as anticategoria).
Examples
[the struggle for women's voting rights] was one of America's most divisive philosophical wars. But it was a bloodless war. Hillary Roddham Clinton, "Remarks to the U.N. 4th World Conference on Women Plenary Session" (5 September 1995)
The growth in these Federal programs has — in the words of one intergovernmental commission — made the Federal Government "more pervasive, more intrusive, more unmanageable, more ineffective and costly, and above all, more accountable" [sic].
Well let's solve this problem with a single bold stroke: the return of some 47 billion dollars in federal programs to state and local government, together the means to finance them and a transition period of nearly years to avoid unnecessary disruption. Ronald Reagan, "First State of the Union Address" (26 January 1982)