Q : Isn't it irrational to believe contradictory things?
A: Yes, but sometimes bundles of ideas get caught up together. We assume that X iff Y. And that X and NOT Y are inconsistent. But it's sometimes worth looking into this carefully. Then you find X doesn't iff Y, and that there's an interesting position which combines X and NOT Y.
But remember the DevilIsInTheDetails.
This maches nearly exactly with De Bono 'lateral thinking' methods - like starting with some provocative statement (like: let's have cars with square weels) then look where it would lead us. I think this is like seeking maxima of some regular but very complicated function where you can't just rely all the time on current gradient to lead you, but you have to do jumps from time to time.
See also FalseDichotomies