You cannot be “in an argument.” You can be “in disagreement” when in an argument there is disagreement or misunderstanding.
In a discussion the other day, a friend asked me to pretend that I was doing a performance review on POTUS. His argument was based on that premise, and the subarguments were 1) POTUS is a CEO, 2) the “economy” is “good,” and 3) there are “jobs.”
I refused to take the bait. Ayn Rand would have been proud of me because I considered the premises.
An argument is a proposal passed to a discussion. Both interlocutors can be in agreement, in which case the discussion is short. Or the receiver can reject the argument, rightly or wrongly — and a discussion never takes place. Or the discussion descends into a disagreement — and the discussion concludes, eventually, beside the point of the argument.
An argument is a proposal for an agreement, otherwise it is aggression.
— Kilgore Forelle