Paradox Thinking

The basis of paradox thinking is
"... Instead of presenting evidence that contradicts someone's deeply held views, a psychologist agrees with a participant, then takes the view further, fetching their arguments to the absurdity. This causes the participant to pause, reconsider, and reframe their own beliefs..."
Olivia Goldhill, 2019
This technique is being used in Israel to try to help resolve Israeli-Palestine conflict; it was initially used in the 1980s to change people's views about societal gender roles.
It has been found that people exposed to paradoxical thinking
"...developed a more consolatory attitude about the Israeli-Palestinian conflict, and were more likely than a control group to vote for dovish parties in the Israeli elections..."
Olivia Goldhill, 2019
There are clear psychological reasons people hold fast on their beliefs; there are psychological needs to be met, ie people have a deep-seated desire to believe their opinions are moral and correct.
"...If you want people to change their views, there is nothing to be gained by labelling certain opinions as 'stupid' or 'evil'. If we dismiss their needs, and say it is only a conservative view, we'll never be able to create anything different than what we have now..."
Ben-yair as quoted by Olivia Goldhill, 2019
Summary
"...telling people they are wrong and presenting evidence only makes them more defensive. Paradoxical thinking creates far stronger results..."
Olivia Goldhill, 2019
Furthermore, if you try to convince people only by facts, logic, etc, most listeners will 'cherry pick' the facts, etc that support their point of view. 
Using paradox thinking is a way to get people to listen to you. You first need to get their attention in a positive way, ie acknowledging their point of view as important and relevant. Once you have their attention, then you can discuss the ramifications and consequences of their point of view. Most people do not appreciate the ramifications and consequences of their points of view. Once they understand this, you then have more chance of getting them to modify their point of view, ie they did not fully appreciate the possible ramifications and consequences, especially negative, of their point of view.