As Edwin Ashworth suggests in a comment above, the formulators of this GRE test question must be relying on a difference in collocation between (on the one hand) "bitter arguments" and "acrimonious arguments" and (on the other) "astringent arguments."
A Google Books Ngram chart for "bitter arguments" (blue line) versus "acrimonious arguments" (red line) versus "astringent arguments" (no line, due to "Ngrams not found") shows the preferences of writers represented in the Google Books database over the period 1900–2005:
But this is far from saying that "astringent arguments" is outlandish or incoherent as an expression. Google Books searches for "astringent argument[s]" turn up a number of matches from presumably competent English speakers and writers, going back to this instance from the speech of Henry Brougham, counsel to Queen Caroline, in "Bill of Pains and Penalties against her Majesty" (August 17, 1820), reprinted in The Parliamentary Debates from the Year 1803 to the Present (1821):
But how can your lordships be reconciled to such a deed [divorce] in the extraordinary manner proposed by this bill, where the husband himself does not, as in every other instance of divorce, come forward to make any application for the measure? My learned friends on the other side, in order to get rid of the astringent arguments which they had reason to apprehend upon this point, on the part of my client, have, no doubt, told your lordships, that the king [George IV] is no party to the present application. But my learned friend, the attorney-general, when certain questions were put to him, could hardly tell whence he came, how, by whom he was sent, or with whom the present prosecution originated, although he could say that the king was no party to the measure.
Also noteworthy is this instance from James Baldwin, "The Black Boy Looks at the White Boy" in Esquire (May 1961), reprinted in The Price of the Ticket: Collected Nonfiction, 1948–1985 (1985):
Norman [Mailer] has many qualities and faults, but I have never heard anyone accuse him of possessing this particular one [an inability to anticipate people's reactions to his work]. But Malaquais's opinion seemed to mean a great deal to him—this astonished me, too; and there was a running, good-natured but astringent argument between them, with Malaquais playing the role of the old lion and Norman playing the the role of the powerful but clumsy cub. And, I must say, I think that each of them got a great deal of pleasure out of the other's performance.
There even happens to be an occurrence of the phrase in a periodical from the Scottish Academic Press titled The Use of English (1985):
Lack of space prevents me from doing justice to the astringent argument and style of Mr. Lee's reevaluation. 'What can be said ...?' etc. came up in an exchange of correspondence in 1979.
"Astringent arguments" is clearly not a meaningless phrase in English. Consequently, the basis upon which the GRE test formulator deems "astringent" an incorrect answer to the given fill-in-the-blank question must be that "bitter arguments" and "acrimonious arguments" are far more common in written (and presumably spoken) English than "astringent arguments" is.
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