The narrator notes that the brain functions faster while it's falling. Because of this, after Ove kicked his stool, he had a lot of time to think about radiators. The narrator says that the feud between Ove and Rune had been about a new heating system for the houses in the neighborhood, though it was really about many things and spanned 37 years. Ove can't even remember how it started, but it also had to do with cars. In the beginning, Ove and Rune had been friends for the sake of their wives, who became best friends immediately.
Ove and Rune's friendship came about because of their loyalty to and desire to please Sonja and Anita. In many ways, this speaks to the strength of their relationships with their wives, as both Ove and Rune seem similarly principled and solitary. The fights about heating systems and cars suggests that their firmly held beliefs didn't line up with each other.
Ove and Rune had developed the Residents' Association. Ove was the chairman and Rune was the assistant chairman, and the first major thing they did together was shut down the city council's plan to cut down the nearby forest and build more houses. The war with the council went on for a year and a half, but Ove and Rune won. They didn't seem particularly happy about winning, but that's because that year and a half of fighting made them exceptionally happy and they were sorry it was over.
Initially, both Ove and Rune fought for the good of the small community and neighborhood by fighting to keep the forest. Notice that their adversary in this fight is the nameless, faceless council. This suggests early on that it is possible to win these fights against the council and the white shirts. It then provides Ove hope for the future that he can win again.
Rune bought his BMW long after that and Ove thought he was an idiot for doing so. Sonja only rolled her eyes at Ove and called him hopeless, but Ove thought that Rune's switch to BMW was an indicator of a lack of loyalty. He thinks all this as he's falling and also thinks that nobody can change tires or file their own taxes. Today, Ove doesn't know if Rune even has the BMW because he's ill and doesn't leave the house. He thinks that he misses Rune all the same.
Ove's principles certainly don't allow for anyone to switch car brands, especially when they switch to a foreign brand. Notice too that in Ove's "final moments," he's also ruminating on the fact that people can't do things for themselves anymore. This is extremely offensive to him and makes those people less valuable in his eyes.
Ove falls and hits the ground. He swears when he realizes that his rope broke, which he thinks is an indicator that nobody can manufacture anything of quality anymore. Angrily, Ove cleans up his plastic sheeting and puts his drill away. He grabs his watering can out of the shed and knocks on Anita and Rune's door. When Anita happily opens it for Ove, he grumpily asks where the radiators are and says his day is already ruined.
When Ove's attempts to die are thwarted, he turns to the community (though he only does so grumpily). Performing these acts for the community allows Ove to feel superior, as he's the only one capable of performing them as far as he's concerned. It also has the side effect of giving him the opportunity to see that he's needed in his community.