I don't know why there wouldn't be a rational reason to think logically; maybe I'm conflating the technical sense of "logically" with some other sense. To the extent that I even understand the question, I suspect that the "companions in guilt" problem might be of a piece with an argument from metaepistemology:
Whereas Boghossian’s wider objective in defending (a version of) metaepistemological realism was to press back against “postmodern” thinking in the academy, Terence Cuneo’s (2007) defense of metaepistemological realism also comes in the service of a further objective, in Cuneo’s case, a defense of metaethical realism. Cuneo’s master argument is as follows:
- If moral facts do not exist, then epistemic facts do not exist.
- Epistemic facts exist.
- So, moral facts exist.
- If moral facts exist, then moral realism is true.
- So, moral realism is true (Cuneo 2007: 6)
Because Premise (2) is his central focus, Cuneo’s case for metaethical realism largely boils down to a sustained defense of metaepistemological realism (see also here Cuneo & Shafer-Landau 2014). Also, like Boghossian, Cuneo’s case in favor of metaepistemological realism proceeds as a negative case against various forms of metaepistemological anti-realism, including especially error theory and expressivism...
Or maybe the normativity of logic is relevant (c.f. the question of semantic normativity).