After reading the comments I noticed that I had at least two distinct mental processes that I'd been labeling "rationalization".
Process 1: Say I'm late for a meeting, I have noticed that in thinking about saying "Sorry, I'm late" I immediately want to add an explanation for why this isn't my fault.
Process 2: Someone presents an argument for a conclusion I disagree with, I immediately start looking for flaws in it/reasons to dismiss it. As I observed here, this is necessarily even a fallacy.
Anna Salamon and I are confused. Both of us notice ourselves rationalizing on pretty much a daily basis and have to apply techniques like the Litany of Tarski pretty regularly. But in several of our test sessions for teaching rationality, a handful of people report never rationalizing and seem to have little clue what Tarski is for. They don't relate to any examples we give, whether fictitious or actual personal examples from our lives. Some of these people show signs of being rather high-level rationalists overall, although some don't.