Well, some do it because they have a very strong territorial urge and see the cars as a trespasser. Some do it because they have a high prey drive and see the cars as “hey, it runs, I must chase it.” Some do it because they’re terminally stupid. 
I had a high-prey-drive dog that wanted to chase cars, bikes, anything that moved. He couldn’t because I always had him on leash, but he never got over the urge.
I remember one day having an SUV drive past us and stop at the site where the mailboxes for our street are located (we’re on a rural route). As we passed the parked SUV, Idol reached out and bit one of the tires. I guess he figured he finally caught himself some ‘prey.’ 
I have noticed sometimes they do it at random… like suddenly running after a car in a street full of cars and chasing for a minute and then calmly walking back …
dogs are very funny …
My border collie chases cars because she was born to herd and contain everything that moves. Dogs with high herding drive are often the unfortunate victims of squishings on the road.
I had a dog once that was so stupid, it chased parked cars.
My beagle chases loud cars, bikes and motorcycles. He also hates open vehicles like mail delivery trucks and jeeps. I always figured he thought the vehicles were growling at him.
My beagles can not see other cars. They would walk straight across an expressway.
Well, fortunately, my dog is scared of cars (but not of riding in one. She loves that.) But even though she’ss been raised with my cats, if one of them runs, she has to *has to * **has to ** chase it. And when she’s on leash, and I’m walking her, it’s so easy to see her mentally start to go after a rabbit or squirrel, and then remember she’s leashed.
Dogs chasing cars are like me chasing 19 year old girls. If they ever caught one, they wouldn’t have a clue what to do with it.
Come to Thailand.
I was a teenager when my dad once asked this question in exasperation when we drove past a yard and soon had a bunch of yapping dogs chasing after us.
I said, “I dunno, I guess it’s just their instincts.”
To which my dad replied, “Well, my end stinks too, but I don’t chase cars!”
This, of course, drew loud laughter from all of us kids in the back seat.
I rode my motorcycle to a friend’s house one day and their little cowardly beagle mix dog that hangs around had a fit when I pulled up, barking and running away from the motorcycle. I went inside and the dog kept barking and yapping at my parked bike. Her owner finally had to go out and tell her it was ok.
Sausages! Sausage! Sausage! Sausages!!
I LOVE that commercial!
We just rescued a young Bichon Frise. He thinks that he’s a REALLY BIG DOG, although he’s only 11 pounds. Whenever we are out for a walk, he lunges with all his strength whenever a car drives by, the bigger it is, the harder he pulls. I’m really going to have to break him of this, because if he ever gets loose, he’s going to get killed by the first car that drives by.
I used to have a problem with my dog lunging and growling at cars when the passed by while we were taking a walk on our semirural steets.
Then somebody suggested some behavior modification. The dog was aggressive towards cars because I was tensing up when the car passed by, because I was afraid the dog would be aggressive toward the car, which the dog interpreted to mean that the car was dangerous and we were going to have to fight it.
So whenever a car passed by, I would cheerfully say “Good car! Good car!” and pretend to be happy to see the car. And the aggressive behavior towards cars suddenly stopped.
It’s amazing what we communicate to dogs that we don’t mean to.
Many dog trainers will tell you: what you feel goes right down the leash.
This is often why some dogs also become “leash aggressive” and territorial towards other dogs or even strangers when they’re out walking on leash but are otherwise fine when off leash. Owners tense up and reel them in so they’ll behave… but the dog misinterprets the cue.
The same is true about obedience trials. If you’re nervous before going into the ring, your dog feels it, all the way down the leash. That’s usually when they start to freak out, too. OR that’s when they’ll choose to behave like total morons, just to blow off that elusive third leg you need to get that title you’ve been working on together. Of course. 
Hee.
As for the OP: The question has been answered. In short, it’s prey drive. Cars move. Dogs chase because of prey drive. Must chase thing that moves. Gaaaah.
I had a terrier who was horrible about it until the one day she hit a truck. A moving-van driver saw her dart out of our yard, stopped as to not squish the dog… but the terrier hit a tire. By that point, I’d heard the tires squeal, realized the dog was out of the yard, got out the front door and heard the dog yelp… Suddenly this ball of black and grey fur ran by my feet like a demon on speed, zoomed up the stairs and hid under my bed. She limped for a week. (Yes, we had her checked out! Nothing broken.)
Little shit.
Link please …
My dumbass dog doesn’t chase moving cars, but she tries to get IN to the cars.
She thinks that every car is there to pick her up and take her on a R-I-D-E so if a car drives by us while we’re walking I have to rein her in or she’ll start hopping up on the window asking to be let in (people drive slow in our neighborhood).
She also really, really likes to smell fenders in parking lots. I like to take her up to the high school during after school sports and let the kids think she’s sniffing for drugs.