Written by the band and produced by Emile Haynie, "Breakin' Point" is a midtempo pop song with lyrics alluding to the protagonist's concerns about expecting a child.

It features a whistling intro, which the band were initially hesitant to include as their breakthrough single "Young Folks" (2006) had a similar composition.

[2] Initial sessions with Patrik Berger aimed to create a "classic" and guitar-focused sound, but the band soon changed their approach to make "the best possible pop songs".

[2] Yttling felt an "Emile Haynie beat" would fit the song and reached out to the producer, who was visiting Stockholm at the time and agreed to work with them.

[4] As "Breakin' Point" was conceived near the ten-year anniversary of Writer's Block, Morén described the whistling aspects as a "nice tribute" to "Young Folks".

[8][9] Rose Kerr of Spectrum Culture observed the song's "darker" beat in contrast to its whimsy provided by whistles and a "backing youth chorus".

[7] Clash's Will Butler viewed the lyric "Got it from whisky like any loser can" as Morén "tacitly" evoking a "part-Hunter S. Thompson, part-Brian Wilson persona".

[12] Regarding its lyrical theme, Morén told Stereogum it has several meanings, "It's about waiting for new things coming ahead that will leave the past in the dust or at least make it look very different.

[16] Both bands utilize Ingrid Studios in Stockholm, and Yttling told Consequence of Sound that "it was exciting to hear [Miike Snow's] take on our song".

Michelle Geslani of Consequence of Sound hailed it as a "lovely number uplifted by a harmonious mix of sweet whistling, reverberating drums, and a swelling chorus".

[14] Drowned in Sound's Kellan Miller wrote that the song "manages to distinguish itself as its own unique, borderline magnetic offspring", despite exhibiting similar "contagious" whistling as "Young Folks".

[21] In a negative review, Tim Sendra of AllMusic felt the whistling is a "sad reminder" of "Young Folks", and regarded it a low point on the album.

[26] HochR wanted to capture a modern take on Hades and avoided a "typical dark, burning underworld", instead opting for a "seemingly fairytale forest" and "sunny sand dunes".

He meets a ferryman by the river of Styx and boards a ferry, taking him to a forest where he is accompanied by his "inner fable animal",[27] a creature with long fur resembling yarn strings on a mop.

Tom Breihan, writing for Stereogum, named the visual the fifth best music video of the week of its release, asserting "The final reveal here is a good one, and it makes me wish I had my own mop creature.