That phrase helps crystalize the concept very nicely.
The ability to entertain multiple, seemingly contradictory thoughts at once is a good skill I think.
That's the academic concept of discussion, which is a very fine and respectable (not to mention important) thing.
Sometimes you do have to persuade, because action is required.
For instance, it is important to persuade non-believers in human-caused global warming; it's not just about improving their intellectual position.