Yes. I will give an example. I assume you are familiar with the concept of reasoning by analogy, also called Argument from Analogy. It is a form of inductive reasoning which is, obviously, a kind of reason. But analogy is not deductively valid. So an argument that employs analogy in an essential way is rational but not valid. There are many other forms of reason that people employ all the time that are not deductively valid.
So "choice" or "preference" simply shouldn't be used in the same sentence as "rational."
That's wrong too. Very often I make a choice after careful consideration of the consequences and try to, for example, maximize return or minimize cost or risk or some such. It is therefore based on reason. But it is still a choice, after all I could have still chosen the other way despite the argument (e.g. I might do it out of spite or simply because the mood strikes me). Since it is both rational and a choice what else should one call it but a rational choice?
That's wrong too. Very often I make a choice after careful consideration of the consequences...
True, but even a monkey knows not to take the alpha-male's banana because he doesn't like being savagely bitten. Ultimately, every choice boils down to a purely subjective preference concerning expected outcomes. You think A will make you happier than B, so you choose A.
The choice itself is non-rational. "A" might be, "do a rain dance," and you might indeed have reasoned to yourself that a rain dance will bring rain, which will bring crops, which will bring wealth, which will bring women flocking round--so in your mind, "do a rain dance" is equivalent to "get lots of women." But however you might rationalize the significance of "A", you pick it because you want to.
Since it is both rational and a choice what else should one call it but a rational choice?
Thinking was in there somewhere, but not in the act of choosing itself. This is in fact important, because everyone who speaks of "rational choices" invariably commits the same fallacy. Namely, they proceed to equivocate between "logical" and "sane" as meanings of "rational," and characterize people as insane whose choices they don't like. This in turn becomes the justification for focibly overriding their choices.
Indeed, that's the argument you're trying to build. You want to say we need government to protect people from their irrational choices, where the plausibility of the argument comes from reading "irrational" to mean "insane". Throw in a pinch of elitism, and we'll readily swallow the implication that everyone in the world (except me) is insane, and needs a government keeper. Bake at 250, and voila! Statist soufflé!
If you try to give an example of the "irrational" choices that justify forcible government intervention, you'll see that I've anticipated your argument precisely.
My reply is not to claim that the man who freely chooses suicide, or self-mutilation, or what have you, is "sane". Rather, my reply is to deny that the man who chooses to wear a suit and go to work is any more "sane"; you just think so, because he's acting so much like you. But ultimately he's just doing what he wishes to do.