[9] Calum Marsh observes that the film applies lofty Wittgensteinian language games to metaphors in cinema and television, and then "it pivots sharply, and becomes instead a character study of a college lecturer with a lot on her mind", an effect "common to all of Cockburn's work: ever restless, he aspires principally to challenge and surprise.

Prince agrees, but is more explicit:Toying with cinema, language, and time, the first half essentially functions as a video essay laying out the professor's argument.

[5] The now "hybrid" film[11] makes further demands through the inclusion of the onscreen annotations: they may be interpreted as the professor's running internal monologue[12] or as her written notes (aide-mémoire),[9] among other possibilities, but regardless, they require "multiple viewings just to decipher it all.

Cockburn originally conceived of the project as a "lecture-performance," like All the Mistakes I've Made:As I worked on it I realized I'd prefer to make it a short film, and to cast someone else in the speaking role.

[20] Two months later, it was screened at a sold-out show at Depth of Field, a semi-annual event showcasing recent York University CMA graduate thesis films in November, at the Art Gallery of Ontario.

[22] The short had its American premiere at the Museum of the Moving Image in Astoria, New York, the First Look Festival, on 15 January 2018, where it was misleadingly billed as a "free-associative interrogation and exemplification of metaphors and their meaning",[23] in an attempt to avoid spoiling the film for the audience.

[24] Norman Wilner, writing for Now Toronto, describes The Argument (With Annotations) as a "dry" film "which elegantly knits the semiotics of cinema into an understated relationship drama about an academic ... who realizes that her partner ... is kind of a tool.

[3] Courtney Small calls it "a smart, witty, and at times dizzying, exploration into language and cinema", and a "stirring look at how we interpret words and how easily we accept things not actually said.

Written notes appear on screen as the filmmaker begins to refine her theories and question the accuracy of some of the points she has made... After seeing The Argument, we kind of wish all essay films had a similar second half, with the likes of Adam Curtis and Jean-Luc Godard forced to reassess their intellectual leaps.