Self driving cars might be still far away, despite the promises the automakers make that we'll get them in three to five years. There are some big technical challenges for sure. But the biggest challenges aren't technical at all.
In normal conditions an autonomous car can already beat a human driver. Only in the more unclear situations is the human reasoning still outperforming machine predictions. But those scenarios also assume the human specimen operating under optimal conditions.
But our performance can vary a lot from those optimal conditions. We get tired, angry, distracted or any of the other humane qualities we have. The computers in the car isn't affected with such "weaknesses". It will continue operating with optimal performance no matter what.
Both have their strength and weaknesses. The technical performance of a car can outperform that of a human where human wins on reasoning.
An accident involving self driving car is front-page news material. It's something that doesn't happen every day unlike fatal accidents involving human drivers. Of course there are way less of the former ones on the street. But they won't be accepted until it's no longer news that they have killed somebody.