I still don't understand why cars aren't using asymmetric keys
Because the branch of the threat tree that asymmetric cryptography would protect against, which isn't protected by a pre-shared secret assigned when the car is manufactured, is largely negligible, and doesn't justify the additional fragility and power consumption that would be added to the key fob. Asymmetric cryptography isn't some magic solution to everything. It's primarily useful when there's no secure channel for initial secret agreement, and for cars there is: it's called the factory.
That's assuming asymmetric cryptography would be implemented properly, with a protocol that actually provided additional security. And that's pretty damn unlikely when we're talking about auto manufacturers.
Asymmetric cryptography wouldn't help with relay attacks, which are the most common attacks against the unlocking protocol. What does help with relay attacks is requiring user interaction on the key-fob end, but we can't have that because people are too damn lazy.
And, of course, this attack has nothing to do with defeating the unlocking protocol.