An Argument with Myself received generally positive reviews from music critics. At Metacritic, which assigns a weighted mean rating out of 100 to reviews from mainstream critics, the album received an average score of 76, based on 12 reviews, which indicates "generally favorable reviews". Erik Adams of The A.V. Club gave it a B rating and praised Lekman's songwriting as "so detailed and so personal". Zachary Houle of PopMatters called Lekman "one of the most dependable and vital songwriters at work today" and stated, "this extended play sees Lekman reaching a transitional state in his songwriting, looking back to past totems used in his work but also looking forward to a new form of expressionism in his songwriting." Jason Ferguson of Paste called the EP "a pleasantly jumbled affair that shows Lekman’s lyrical facility continues to improve, while his stylistic palette continues to broaden", commenting that "he has moved well beyond the simple, twee clone-work of his earliest releases."
Pitchfork Media's Brian Howe called the EP "a compact gem" and stated, "It tilts this way and that to show different facets of the singer: his ruminative side, his topical side, his devotional side, his wicked humor, skewed insight, and flawless banality. At less than 18 minutes, there isn't a wasted moment. Each song does something distinct both sonically and lyrically, filtering one rarified but relatable sensibility through guise after revealing guise."Consequence of Sound writer Austin Trunick stated, "Full of the poppy arrangements that characterized his last album, there’s enough of Lekman’s trademark wit and self-deprecation on display in this 17-minute set to remind listeners of his status as one indie music’s best storytellers." In his consumder guide for MSN Music, critic Robert Christgau gave the EP an A rating and quipped, "The first three songs on this EP are strong, the fourth misty, the fifth sweet and slight, but all know melody and all fill out a portrait of a young man your daughter should only bring home to mother."
However, Embling of Tiny Mix Tapes criticized it as "less than the sum of its parts" and found Lekman "in an even more exaggeratedly stilted, self-amused state than ever", stating "Whereas self-deprecation was once among his most endearing qualities, now Lekman comes off as debilitatingly insecure."Allmusic editor Tim Sendra commented that the songs are "a bit too sophisticated, as it’s the first time Lekman's records have sounded played by professionals instead of pieced together with samples or stumbled through by friends, and inspired instead of painstakingly crafted. It gives the songs a sheen of studio gloss they don’t need at all and distracts from Lekman’s innate humanity and the intimacy he so easily transmits most of the time." Gareth Ware of MusicOMH viewed that "musically [...] parts of the EP leave a lot to be desired," although he commented that "Lekman's ability as a raconteur extraordinaire remains undimmed."Drowned in Sound's Sam Kinchin-Smith noted "no one big overarching idea, no head-explodingly poptastic lead single" in comparison to Lekman's previous EPs, but commended him for "mak[ing] songs out of fragments rather than sweeping panoramas: of other people’s songs, of dialogue, of stories from his own life, of stories from others'."