Most likely an autonomous car can react quicker to an obstacle running in front of it faster than a human can.
With the added bonus that if the computer doesn't react fast enough, it won't drive off and leave the pedestrian bleeding in the road to protect its insurance premiums or hide the fact that it's had a few drinks before setting off.
Compare that to a pair of forward facing eyes, with an elaborate system of mirrors to try and allow them to see behind the car as well as in front. Lots more blind spots, and they can only look in one direction at a time.
And there are lots of drivers incapable (at least for periods) of even managing that. The one huge benefit of this system is that it never gets distracted by something on the radio, or the phone ringing, or wondering what to pick up for dinner, or by the idiot who just cut it up. I wouldn't be surprised if the vast majority of accidents are caused by momentary lapses in judgement (there will be a lot that are caused by plain old bad driving, but over time experience, the legal system, and ultimately crashes, should weed those out).
What is this mental disease that makes people think we should fight to have billions and billions of people live forever?
I think it's called "humanity". You are right that it's cold logic, the head and not the heart, that will solve these issues, but for most people it's not so easy to divorce the two concepts; to know you have enough to live comfortably and to watch children starve.