It is a long-known and bitter fact that when automobile manufacturers design a vehicle, they compute how many deaths each feature will cause or prevent and decide cost/benefit for each. As long as we live in an unpredictable world, automobiles, trucks, SUVs,
et al. are going to kill people.
If anything, self-driving cars are less likely to kill people. They don't attempt to apply makeup in the rear-view mirror, they don't talk on the phone while driving - or if they do, it's not a distraction at least. They don't experience road-rage. They don't drop hot greasy fries in their lap and juggle picking them up and grabbing the steering wheel.
However, the operative
word there is
learning. And remember that virtually all news is based on the unusual. We have vehicular accidents all day every day, but only the unusual ones get special attention. With self-driving cars being relatively new and rare, every accident involving one will get outsized attention, even as the anti-shutdown demonstrators overshadow the much larger crowds of people who don't go out and spread the "love".
As long as vehicles continue to learn, they become progressively safer, allowing for the fact that some situations simply cannot be made safe short of having Superman fly in and lift away a car that cannot find room to stop or swerve. There is after all, a point of diminishing returns and the old "which way to switch a streetcar" philosophical problem has no simple answer.
I think it's generally accepted that traffic would be safer overall if
all cars were self-driving. You'd still have external events, but at least then the automated cars could proceed on the basis that all the other cars were being driven rationally.
Some people, when well-known sources tell them that fire will burn them, don't put their hands in the fire.
Some people, being skeptical, will put their hands in the fire, get burned, and learn not to put their hands in the fire.
And some people, believing that they know better than well-known sources, will claim it's a lie, put their hands in the fire, and continue to scream it's a lie even as their hands burn down to charred stumps.