> why did your self-driving car hit that pedestrian?
It didn't see him/her. Which is the extent of an explanation a human can give you. Try to picture wanting a person to explain why they didn't see a person coming from the side. We don't know what's happening inside our own heads.
That's my point - we're recreating an inherently non-explainable system in software, because we can't explain how it works. The algorithm is so complicated, we can't code it explicitly, so we let the machine figure out the semantic-free equations. All is not bad though, you could always dry-run the algorithm at home, i.e. ask your car "how visible am I with these clothes on", and just not walk outside with low-visibility and low-recognition clothes. Some countries already require pedestrians to wear reflective clothing in the evening to make themselves more visible. I suspect we'll have similar rules for self-driving vehicles: you must wear recognisable clothing when walking through traffic.
What I mean about "what if you don't like the explanation" is something else. Let's say you use a deep-learning software to determine sentences. The software spits out "5 years, because this is a black male". Do you accept that? It has been proven effective in many previous cases, can you accept that it has independently discovered a correlation between the person being black and the length of the sentence? Let's say you entirely remove the person's colour and sex from the dataset and re-train, then it will give you shorter sentences than you expect, because every judge previously had subconciously taken all these variables into account. Or it will discover a correlation between wearing e.g. adidas and alcoholism because Slavic people have a higher rate of alcoholism and wear adidas more often than others.
Which comes back to my core argument: If you know the acceptable metrics and algorithms, why are you using deep learning? If you don't know the acceptable algorithm, how can you verify the explanation?