Last year, or the year before, there was a murder in Iceland and it made national news. Why? Because there are virtually no murders in that country - it is an exception to the rule.
Mile-for-mile, self-driving cars fare significantly better than humans: who are actually the ones "mowing down people." Especially the drunk ones. It's exactly the same situation as Iceland with the murders, if you had national news each time a human caused a casualty there would be hardly enough time to tell the news.
The "mowing down" hyperbole is doing your cause no justice. I certainly agree that it's too early to go completely driverless (especially when your trustworthy humans go hands/eyes-free in cars that explicitly disallow it) - but humans have never had the qualifications to deal with something that drives 10x the speed than they can sprint.
If you want to pull self-driving cars off the road then, great! I think we can all agree with that. Let's pull all human drivers off the road first - not only do the statistics support that we're incompet, biology does too.
I've never had issues with it because it shuts off when indicating in the direction that you are turning.