I've said this before - I used to have a pit mix (departed now). She was animal aggressive. We should have socialized her better, but didn't realize the problem until it was too late - she was friendly with puppies and with our other dogs that she grew up with. But the point is, that I could - and a couple of times, had to - put my hand in her mouth, with complete safety, to pull her off another dog. The other dogs (never another pit/mix) bit me, you bet. (These were off-leash dogs that approached her when she was at the end of our leash. Not something we could avoid except by never walking her.)
That's a classic pit personality (even though she was a real Heinz 57 and the PB genes were less than half her makeup), and it's what they were originally bred for - to be aggressive with bulls and other dogs, but 100% docile and controllable with humans.
I probably get chased more by herding breeds (Aussie cattle dogs in particular) than by any other dogs. A lab mix followed our club ride for a good two miles a couple of weeks ago.
And no dog should chase anything/anyone on the road, regardless of breed.