At various points during the past forty years, a neighbor would ask Sonja why Rune and Ove hated each other. Sonja usually offered an account of their vehicular upgrades over the years, with Rune purchasing Volvos and Ove purchasing Saabs, until one day Rune purchased a BMW. Ove insisted you can't reason with people who purchase BMWs. Sonja told the neighbors that you either understood it or you didn't. Ove said that people had no sense of loyalty anymore and just viewed cars as a means of transportation.
At this point in the explanation of the Ove/Rune conflict, it appears as though it's simply a matter of Rune's faltering loyalty to a Swedish car brand. To be fair to Ove, this has already been developed as a major offense in his eyes. He also views cars as almost living things and certainly as a connection to his father, hence his lament that people don't view them in that way anymore.
Back in the present, Parvaneh tries to get into Ove's car with a bottle of fizzy juice and then tries to change the radio station, both of which are bad ideas according to the narrator. Ove instructs her to press the clutch pedal. Parvaneh looks around and asks where it is, and Ove holds his forehead. Parvaneh looks sour and says she wanted to get her license for an automatic, but Ove yells that she's getting a "proper license." They shout at each other for a minute and then Ove tells her where the clutch, brake, and gas pedals are. He explains how to get the car to move. Parvaneh does as she's told and the car lurches forward. Ove pulls the hand brake as the car comes within inches of another car. Parvaneh panics, but Ove calmly says that the car she almost hit is a Volvo and therefore doesn't matter.
Parvaneh's comment about her license type refers to the fact that in much of Europe, a candidate for a driver's license can choose to get a restricted license that allows them to only drive cars with automatic transmissions (a regular license allows you to drive manuals and automatics). As Ove tries to teach, he definitely doesn't remember that driving is something that people aren't born knowing how to do. He does agree to actually teach Parvaneh rather than just act superior, which allows him to continue to build a relationship with her.
They make it out of the parking area and onto the main road. When they reach a red light, a big SUV with two young men inside pulls up close behind Parvaneh. They rev their engine. When the light turns green, Parvaneh promptly stalls the car and the men behind lay on their horn and gesture rudely at Parvaneh. The Saab rolls backwards into the SUV as Parvaneh tries to move off again.
The SUV is symbolic of its driver's rudeness. A car that large can be very intimidating to a Saab, especially one in the control of a new driver. The SUV itself, like its driver’s behavior, is then in violation of Ove's principles and belief in fairness, as well as his new regard for kindness and understanding.
Parvaneh takes her hands off the wheel and starts crying. Ove stares at her in amazement as she sobs that everything is so stressful. The SUV keeps honking. Ove gets out of the Saab, walks around to the driver's door of the SUV, and rips the door open. He yells at the man and pulls him out of the car by his collar. Ove tells the man that if he honks again, it'll be the last thing he does. None of the other cars on the road come to the man's defense, and the man nods. Ove puts him down and gets back in the Saab.
When push comes to shove, Ove shows that he'll stand up for his newfound community members in their times of need. We learn that just like Ove, Parvaneh is putting on a show that makes it seem as though she's collected, in control, and doing just fine—when in reality, that's just not the case. This moment of vulnerability allows the two to strengthen their relationship.
Parvaneh looks at Ove with her mouth open. Ove calmly tells her that he hasn't seen her afraid of anything until now, and driving isn't brain surgery. He continues that plenty of "twits" know how to drive, and she's not a twit. Parvaneh takes this as the best compliment and learns to drive that afternoon.
Ove and Parvaneh learn how to appropriately communicate with each other, which enables them to form a closer relationship and allows Parvaneh to learn how to drive.