Why you have (probably) already bought your last car
bbc.com
bbc.com
In a sense a horse is somewhat 'self-driving' in that an accident could be entirely due to the behaviour of said horse and so this would provide a strong impetus to move to a car which is fully under the driver's control.
Going to a self-driving car shifts back to a system that is not fully driver controlled and thus has to deal with all of the legal issues about who is culpable in the case of accidents and so forth.