Comparing fatalities based on distance traveled obscures the real risks, especially if you do that country-wide: Highways and other long-distances roads are a comparatively safe environment for cars. Accidents are comparatively rare, but often fatal. City traffic differs: speed is in general lower (< 50 km/h), distances traveled shorter and accidents will often not result in injuries for vehicle occupants.
Injuries for cyclists thus are far more likely. Even collisions at lower speed that basically leave a car dented and the occupants uninjured will result in injuries for cyclists: The classic dooring accident, run over by a turning car, etc. Even overtaking the cyclist with too little safety distance can lead to a fatal accident [1]
The stats in Berlin (2015) indicate that while cyclists are involved in about 4% of all accidents, they make up 21% of persons killed (pedestrians are even worse off: 1.33% involvement, but roughly 40% of all persons killed). They also make up more than 30% of all injured (30% of major injuries). Pedestrians make up for 13% of the injuries (24% of major injuries). So the group of soft targets that is involved in roughly 5% of accidents suffers 60% of all fatalities, 54% of nmajor injuries and 43% of all injuries.[2]
The data that was linked to was fatalities per 100 million trips. Unless I've missed something, that's what you want. I'm not going to say that cycling is as safe as not cycling, but it's still quite a safe activity. Your odds of getting seriously injured are quite small.
Injuries for cyclists thus are far more likely. Even collisions at lower speed that basically leave a car dented and the occupants uninjured will result in injuries for cyclists: The classic dooring accident, run over by a turning car, etc. Even overtaking the cyclist with too little safety distance can lead to a fatal accident [1]
The stats in Berlin (2015) indicate that while cyclists are involved in about 4% of all accidents, they make up 21% of persons killed (pedestrians are even worse off: 1.33% involvement, but roughly 40% of all persons killed). They also make up more than 30% of all injured (30% of major injuries). Pedestrians make up for 13% of the injuries (24% of major injuries). So the group of soft targets that is involved in roughly 5% of accidents suffers 60% of all fatalities, 54% of nmajor injuries and 43% of all injuries.[2]
[1] see incident 10 on this list http://adfc-berlin.de/radverkehr/sicherheit/aktionen/62-geis... (sorry, german only) [2] data taken from https://www.berlin.de/polizei/aufgaben/verkehrssicherheit/ve... (sorry, german only)