From a certain POV, we have to think that because of what logic is.
From a neo-Intuitionistic perspective, a la Steven Kleene, mathematics, and logic in particular, is the full elaboration of the set of 'intuitions' or assumptions about ideas that all humans ultimately share. It is the set of things to which we naturally respond with the calm acceptance of the proven, and for which the only challenge to belief is sheer complexity.
There may be some delving about to make us recognize them, but as Plato noted in the Theatetus, they bubble up from inside, or they fail to. And those for whom they fail to are then deprived of a certain part of human cultural experience.
But that means that whatever does not at some level follow the rules of logic and or mathematics is incomprehensible to humans as a whole. So we don't question logic because generally, when we needed to, we are set to be thwarted.
If we admitted logic did not in any way apply to a situation, we would just be sunk anyway.
Humans are often very herd-like beings, and we tend not to care much for what cannot be shared with other humans. So human thoughts that cannot be wedged into accepted logic tend not to matter, unless they pay off in some demonstrable way.
We do make the effort to build up artificial logical approximations to the parts of the world where it pays off to defy our logic. We may find them endlessly fascinating. Many intelligent people in our culture fought with quantum mechanics very hard. Others among us are amazed by our own unconscious behavior or with that of other animals that do not share the logic of our conscious process and yet survive very well.
But we can still only share experiences of those things with one another with great effort and to a limited degree. A large segment of the populace will always consider them a waste of time.