If you ride your bike 3 times a day, every day for 70 years, you have about a 1.6% chance of dying. This is not unduly dangerous.
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)
I love cycling (I cycle a lot), but unfortunately this isn't true. In the US, you are roughly twice as likely to die as in a car[1]. It is much, much, much safer than motorcycling! (Somewhat old data, though)
[1] http://aje.oxfordjournals.org/content/166/2/212.full