The phrase "argued at one point" is correct and usable in written English.
It can be used when referring to a specific moment in a discussion or debate where a particular argument was made.
Example: "During the debate, the candidate argued at one point that climate change is the most pressing issue of our time."
Alternatives: "contended at one stage" or "asserted at a certain moment".
"We need to make sure we have an economy that is strong and growing," the minister argued at one point.
The lottery's lawyers argued at one point that the Little Tramp was a generic early-century urban figure, neither created by Chaplin nor uniquely associated with him.
Yesterday's decision, written by Chief Judge Judith Kaye, was a defeat for the administration of Gov. George Pataki, which argued at one point that the state was fulfilling its constitutional responsibility by providing poor children with the equivalent of an eighth grade education.
"What would indeed be unprecedented here would be dismissing this indictment on speedy-trial grounds," Mr. Farbiarz argued at one point.
Those Confucian philosophers whose writings had been most enthusiastic about Japan, and so easily appropriated — as was the case with Yamaga Sokô who had argued at one point in his multifaceted philosophical corpus, that Japan, not China, was the true Central Kingdom — have consequently suffered from significant neglect in the postwar period.
"Snobbery is universal," he argues at one point.
"A story matrix connects all of us," Harjo argues at one point.
The CPS spent more than two years trying to prevent their release, arguing at one point that the information was Griffin's sensitive personal data.
We're nobodies in our homeland, Houellebecq argues at one point: "We're not even mentioned in the credits of Ratatouille".
"I gave him the best advice and counsel that I could in private," Spicer tried to argue at one point.
"[W]e don't care about Emma Bovary or Anna Karenina or Raskolnikov because they're good," he argues at one point.
