I would say nobodies fault unless they indended to cause the accident.

The auto maker is a fault:
Doors do not need to swing open. There are sliding and gull wing options. Perhaps a light on the door that blinks if the driver attempts to open it, alerting an approaching bicycleist.

The government, specifically schools is at fault:
Since the government monopolizes most of the money available for education it is the states responsibility to teach children to ride bikes correctly. Needless to say bicycle safety is one more failing of the school system.

The bicyclist is at fault:
I also suspect the rider was ridin too fast with breaks that were not properly adjusted. And maybe not paying attention.