I sometimes think there are two kinds of people: those that think there are two kinds of people and those that don’t that agree with Socrates (like me) and those that just like to get on with life without any need for introspection (the eponymous protagonist of Nikos Kazantzakis’ novel Zorba the Greek , with his zest for life and distaste for navel-gazing springs to mind).
Perhaps the same justification could be put forward for poetry (at least some forms of poetry), not that it needs any.
My interest in the quote is the reference to poetry, which the author sees as getting its justification, if it needs such, from the principle of introspection. I doubt he'd see that as an exclusive one, but much poetry indeed does look inward.
Perhaps that's one reason why poetry finds such a happy place in Christianity, with such great emphasis upon the mind, motivations, and the evaluation of the inner life. "Examine yourselves," urges the apostle Paul (2Cor. 13.5).
Poetry serves wonderfully as a tool for such analysis, if the utilitarians among us need a rationale for the time and energy spent on its writing and reading. Then, again, maybe poetry was a pasttime of Zorba the Greek, too.