You are sitting there watching a movie as your car drives you down the street. A child pops out from between parked cars and ... your automation software had no way of "seeing ahead" that this would happen. The best it can do is sense something in the road and slam on the brakes. The car behind you ... has no way of "seeing ahead" that your car would slam on the brakes.
But wait, it was only a dog. The choice of running over a dog versus creating a collision with the car behind you (and the one behind it...) a human could make. What will your automation software do?
In case of your typical permanently distracted driver who is likely to kill the kid and kill the dog no matter what, I'd take being rear ended, thank you very much.
You've just made the best argument so far why automated cars shouldn't be allowed on the streets. You have to pay attention so you can take over in case of trouble anyway, why bother with the automation?
Nope. The automation must be designed so that when you need to take over, the car is in a safe state. That's like man-machine interface 101. The whole reason for automation is so that you don't need to pay attention at all, and when you do, you can take your time.
Anyone who thinks that human-created automated driving systems will be perfect and never require instant human attention to avert disaster is the one with zero clue.
This only makes sense if you're a doofus who thinks humans are much better. Nope, they aren't, they kill thousands each month in the U.S. alone, all people with good intentions, all people who think of themselves as above average. Yes, you still have no clue, and you keep showing it left right and center.
Automation doesn't have to be perfect. It only needs to be a bit better than humans in the average case. If all automation does is cut the fatalities-per-mile rate in half, it's a win. It will be much better than that, it won't ever be perfect. Beating humans at the driving game isn't all that hard.