TL;DR: Coleridge means the cause of the criticism of the poetry of Southey, Wordsworth, and himself, which he believes was Wordsworth’s preface to Lyrical Ballads.
The background to this passage is the critical reaction to the work of Robert Southey, William Wordsworth, and Coleridge himself.
He says that the critics wrongly identified these poets as “a new school of poetry” and clamoured against them and their supporters.
(Coleridge derides the idea that they constitute “a new school of
poetry” as “this fiction”, but posterity has sided with the critics on
this: the Lake Poets are now generally seen as founders of the
Romantic movement in English literature.)
The kind of criticism that Coleridge had in mind can be exemplified by a review of Southey’s Thalaba, the Destroyer in the Edinburgh Review for October 1802 (unsigned, but known to be by Francis Jeffrey):
The author who is now before us, belongs to a sect of poets, that has established itself in this country within these ten or twelve years, and is looked upon, we believe, as one of its chief champions and apostles. The peculiar doctrines of this sect, it would not, perhaps, be very easy to explain; but, that they are dissenters from the established systems in poetry and criticism, is admitted, and proved indeed, by the whole tenor of their compositions. Though they lay claim, we believe, to a creed and a revelation of their own, there can be little doubt, that their doctrines are of German origin, and have been derived from some of the great modern reformers of that country. […]
The authors of whom we are now speaking, have, among them, unquestionably, a very considerable portion of poetical talent, and have, consequently, been enabled to seduce many into an admiration of the false taste (as it appears to us) in which most of these productions are composed. They constitute, at present, the most formidable conspiracy that has lately been formed against sound judgement in matters poetical; and are entitled to a larger thare of our censorial notice, than could be spared for an individual delinquent. […]
In the passage from Biographia Literaria, Coleridge goes on to consider the cause of this critical outcry, and rejects three possible explanations: he says that he believes that Southey’s writings were not the cause, nor his own, nor the poems of Wordsworth in the Lyrical Ballads. A couple of paragraphs later, he identifies what he thinks is the real cause:
In the critical remarks, therefore, prefixed and annexed to the Lyrical Ballads, I believe, we may safely rest, as the true origin of the unexampled opposition which Mr. Wordsworth’s writings have been since doomed to encounter.
Wordsworth’s preface to Lyrical Ballads is indeed exactly the kind of manifesto likely to provoke critics to intemperate response:
If in a Poem there should be found a series of lines, or even a single line, in which the language, though naturally arranged and according to the strict laws of metre, does not differ from that of prose, there is a numerous class of critics who, when they stumble upon these prosaisms as they call them, imagine that they have made a notable discovery, and exult over the Poet as over a man ignorant of his own profession.