Dino, people do hold ideas that are contradictory. You mentioned a few examples. As another example, Jefferson's words, "All men are created equal", clash with the culture he was born into. Such contradictions cannot be reconciled, so they are kept apart. Compartmentalization is the fancy term. By embracing each idea in isolation, the contradiction is avoided.
It seems to me that there is a very good reason for not holding two contradictory ideas simultaneously. Thoughts are generally a plan for action, but if one part of the plan says go left and the other says go right, we reach an impasse. Since this doesn't happen very often, there must be some mental mechanism which sorts contradictory items into separate time slots. This allows us to go left then after that to go right.
Most of us are familiar with that drawing which can be perceived as an old woman, or alternately as a young girl. We first see one image then the other, but they do not appear at the same time, in the same thought. What would it look like if they did, a middle aged woman?