The narrator says that Sonja always said that Ove was unforgiving. Ove knew that Sonja was disappointed that he and Rune couldn't remain friends, but Ove couldn't figure out how to fix what happened or even how the conflict started. It ended when Rune bought the BMW. The narrator insists that the connection between cars and emotions is the only thing that explains why Rune and Ove became enemies.
The narrator has already left clues indicating that cars are tied to emotions in the book. Ove's affinity for Saabs is an emotional connection both to his father and to his country, while the man in the white shirt's Škoda is an indicator that he's a powerful jerk.
Not long after Ove and Sonja returned from Spain after the accident, Ove laid new paving stones, Rune built a fence, Ove put up a higher fence, and Rune built a swimming pool. Ove angrily insisted it was just a splash pool for their toddler and threatened to report it, but Sonja shut that suggestion down. Soon, Ove saw a rat and demanded all residents put out poison, but everyone refused. Someone sprinkled birdseed behind Rune's house, which attracted massive rats, and Rune put out poison. There was then the "Snow Clearance Skirmish," an argument over lawnmowers, and "the battle of the water pump" when the houses needed new heating systems.
The fences and the splash pool in particular suggest that Ove is jealous that Rune and Anita have a child, even if Ove isn't willing or able to admit that. Rather than actually talk to each other about Ove's jealousy and their emotions, the men instead use their respective outdoor areas as weapons and as signals to fight each other. They also fight through official channels (it's implied that the heating system question is a question with a single answer for all the houses).
There were good moments in and amongst the conflict where Sonja and Anita were able to get together with Rune and Ove for dinner. When Anita and Rune's son was a teenager they had a dinner and whiskey after, but had a fight over how to light the grill weeks later. Rune's son moved away in the early 1990s at the age of twenty. Anita tried not to cry, and Rune seemed to shrink over the next few years.
These good times show that the men did indeed like each other, but the gulf created by the fight was just too much to get over long-term. When Rune and Anita's son moves away and they struggle, it stands as an equalizer between Ove and Rune: neither has their child.
A few years later, Ove and Rune fought over the heating system for the last time, and then over Rune's new robotic lawnmower. The lawnmower mysteriously drove itself into Rune's pool and weeks later, Rune went into the hospital and never bought another lawnmower.
The breakdown of Rune's family brings about his poor health and the end of his feud with Ove. Everything unravels after Rune's son's departure, as the stable family unit is necessary for keeping its members healthy and happy.
The narrator explains again the men's string of cars: cars to accommodate strollers and wheelchairs and more children that never arrived. The narrator wonders if Ove never forgave Rune for having a son he didn't get along with, or if neither man was able to forgive themselves for being unable to give their wives more children. After Rune's son moved out, Rune bought a sporty BMW with two seats since it was only him and Anita. Ove realized that Rune had given up on having a family.
Here, we realize that the men aren't just loyal to the cars themselves. Rather, they use the particular car to show that they're loyal to their families and what their families look like at any given time. The two-seater BMW is thus a rejection of family, and as a sports car, it's very much just a vehicle to get from point A to point B in a fun and zippy way. It's not functional—it's fun, which is something Ove can’t approve of.