The phrase "argued themselves" is correct and usable in written English.
It can be used when referring to individuals who have engaged in a debate or discussion, often emphasizing their own position or perspective.
Example: "In the heated debate, the participants argued themselves into a corner, unable to find common ground."
Alternatives: "debated among themselves" or "contended with each other".
"These two guys more or less argued themselves, on a strictly theoretical basis, into making out.
Yet here they were, cramming into the wood panelling and neo-gothic vaults of the Royal Courts of Justice, hearing Igor Judge, the lord chief justice, calmly reading as a judgment much of what they argued themselves, to no avail, all those lost years.
The FTC also noted that in other cases, the FTC and Department of Justice had argued themselves that search advertising was a distinct product market, including when Google benefited from the distinction in arguing that its purchase of the display advertising company DoubleClick had no antitrust implications since it was in a distinct market from Google's search advertising business.
The difficulties will argue themselves.
P7 David Aaronovitch: Hacked Off argue themselves into the gutter.
Until they do, they will continue to argue themselves into political oblivion.
The most exciting action in "Much Ado" is the way Beatrice, a diva of withering disdain, and Benedick, a maestro of gruff misogyny, argue themselves into a state of starry-eyed mutual infatuation.
The work that made me realise Chaucer was not all horses and castles was Troilus and Criseyde, the greatest account you will ever read of people arguing themselves and each other into and out of love.
With its empirical and historical evidence thickly wrapped in a committedly conversational tone, it's particularly well suited to younger readers who are interested in science, sex and therefore, as Bering would argue, themselves.
Beltway politicians and economists can argue themselves silly about the impact of the Obama administration's stimulus program, but outside the beltway the discussion is largely over.
Yet, Lofton wonders out loud if the standards are so high they "argue themselves out of mass acceptance".
