Cleanth Brooks was a literary critic who had some success with programs making poetry more intelligible & apprciable to undergraduate students and who, I guess emboldened by this success, wrote a number of books discussing poetry. What he wanted to achieve in so doing is not exactly clear to me -- this book's main thesis is that paradox is a principle element in all great poetry, and proceeds by discussing ten poems (or rather eight lyric poems, Pope's Rape of the Lock, and Macbeth) and exposing the paradox employed by their authors within each work. In some cases, as in Donne's Canonization or Wordsworth's Childhood ode, the paradox turns out to be a more or less a pointing-out that the poem's course of argument is incoherent, and that its nevertheless high quality is proof that paradox makes poetry. Elsewhere, he discusses mediocre elements of poetry, such as the repetitive and borrowed imagery of Milton's L'allegro/Penseroso and Gray's Elegy, and claims that the author was being mediocre intentionally, for ironic purposes, and that the coherence of irony itself is a paradoxical. Elsewhere still, as with Pope or Shakespeare, Brooks wisely elects to avoid discussing the frequent rhetorical paradoxes employed by those poets, and instead discusses the uncertainty around which the narrative is built (can Macbeth really gain power? is there substance to Pope's superficially-minded world of manners?) and then claims that these scenarios depict the fundamental uncertainty of life, which is paradoxical for reasons I guess having to do with things seeming one way but actually being another. With Yeats and Keats, Brooks forgets about his metaphor, and spends a while summarizing the contents of the poem and then saying this summary supports the poems conclusion (not at all certain with Keats' Grecian Urne), leaving the reader to infer that Brooks probably thinks philosophical distinctions are inherently paradoxical.
From there, Brooks draws his conclusions: because poetry is poetry, therefore it cannot be represented in any other form than the original poem, and thus all attempts to summarize or paraphrase poems are "heretical" and inherently false. He forgets again about his theory of paradox except for a brief comment, saying at once that the paradoxicality inherent to all poems is proof o this conclusion, but also that his paradox-hunting method also is good because it proves that one cannot summarize poems. Then, with seemingly no relation whatsoever to the rest of the book, he spends a fifty page appendix making pedantic criticisms of rival theorists' attempts to characterize what poetry is -- those who say it is mysterious are wrong because it is intelligible, those who say it is reducible are wrong because it's unsummarizeable. Therefore ... well, no actual conclusion or raison d'etre for this epilogue is given.
I don't understand what the purpose of this book is or why it was deemed worth writing, printing or reading; Brooks summarizes (with varying degrees of competence) ten poetical works, and then comments that poetry cannot be summarized. I kind of agree with his theory of poetic irreducibility, but he argues for it so poorly arguments for the opposite arise -- namely, that obviously one can make a narrative account of the rational elenchus within the poem, stopping to sum up its connotative effects, and then employ it perfectly rationally for the literary criticism Brooks seems to have thought at once totally impossible and yet absolutely necessary ... his feelings about paraphrase are jumbled together with speciously relevant arguments about unique semiotics and the fallibility of translation, which are very valid concerns but far too abstract for concern with literary theory. This he conflates with a Wallace Stevens -like belief in poetry qua poetry, as a metaphysical and inviolably pure entity which he never questions, never discusses, and never seems to have consciously thought about ... in effect, then, his book essentially just iterates that Brooks is a fan of poetry, and so zealously devoted to it that he refuses its sanctimony be questioned at all, while feeling that his (I hate to use the following term) Word Game of identifying paradox within poetries, as scholastic in its refusal to doubt its eventual solution as irrational in its blindness to whatever result it may achieve so long as it can be plausibly called paradox. Indeed, Brooks' bafflingly stupid approach to the phiosophy of language is so sloppy that, taken to its natural conclusion, would present a worldview where any sort of synonymity could be posited without violent refusal, where all writing must be treated as a poetic statement in which one MUST find paradox (as no distinction of poetry from any other form of writing, or indeed speech, seems discernible), and by result communication seems dubiously possible given the impossibility of both definition and coherence.
Ultimately, one can understand why Brooks thought students were unable to understand poetry, given his feelings about the subject, and why he felt that poetic literacy was in decline everywhere. One can, with this being a leading & celebrated critic, also understand why that decline has continued.