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fubarobfusco comments on SotW: Check Consequentialism - Less Wrong
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One of the other models people have for the rationalizing sort of "rationality" is that of lawyers.
Lawyers are very good at logic — the LSAT, the entrance examination for U.S. law schools, leans heavily on logic puzzles — but the whole point of being a trial or appeals lawyer is to come up with clever (and socially respectable) arguments for whatever position your client may have at the moment.
This extends past real-world lawyerhood. The tabletop role-playing game crowd have the expression "rules lawyer" for a person who comes up with clever arguments for why their character should get away with whatever they want to at the moment.
Indeed I think this is the central problem with the way most people use their powers of reasoning. (It even has a name: "the argumentative theory of reason".) They start with a conclusion, and work backwards to find rational (or at least rational-sounding) ways of supporting that conclusion.
We all do this automatically; it may be the very thing our brains evolved to do. We have to work very hard to get ourselves to do the opposite, start with evidence and use reasoning based on the evidence to decide on our conclusion. I'd say most scientists manage to do this right maybe half the time, and most laypeople almost never manage it.