I think if people were given the choice between being rational and being right, they would choose to be right even if that risked sounding irrational.
Appreciating the Difference Between What’s Rational and What’s Right
Holly Wood, PhD 🌹

Rationality is a purely a priori process. By that I mean that it’s the way the brain uses logic to process information. You can be perfectly rational, BUT if the empirical inputs you use aren’t sound, you’ll still be dead wrong.

For example, let’s say you have to find the sum of two amounts, and you get the first one off by one. Your process of addition can function in a perfectly rational way, but if it does so, your total at the end is still going to be one off. Perfect rationality =/= perfect reality.

That’s why science is founded on empirical observation. Rationality can be used to create hyptheses, and to calculate the implications of a conclusion, but to reach a conclusion itself, you need a set of empirical observations as confirmation.