Of the five reasons the only one (to me) that makes sense is the safety issue.
The cost efficiency claim is a bust. I have a 2002 Mazda Protege5 and a 1970 Fiat Spider and according to the article I need to replace them with a new car.
If I purchased a new Mazda3 (purchase price 25K) my basic costs vs. my old cars would be:

The most important reason to keep our old cars is every time we go somewhere, inevitable, someone stops us and asks about our “cool” cars. For most they go down memory lane and tell you a story about when they where young and the cars they had. Plus it is pretty cool to tell them the reason the car is still around is due to your hard work and love for the classic automobile
