I've been road cycling for about 25 years, both commuting and for recreation; I've had only two injuries worth mentioning; both were from falls related to poor surface conditions that I didn't handle well while maneuvering. I've never had a collision with an automobile. I've had one minor collision with another cyclist, a friend who hit the brakes when riding in front of me after asking me what was behind us.
It's my understanding that cycling is generally safer in terms of injury rate per duration of participation than other sports. Bicycling fatalities are rare; they happen, but are less likely than with other popular activities like swimming and motorcycling. taking basic care such as following the road rules for vehicles, behaving visibly and predictably, and paying attention to conditions ahead make cycling even safer than the stats make it look.
A lot of us who participate in safety discussions concentrate on a small number of negative things in order to try to make cycling even safer, through better public education, law enforcement, or engineering. Somebody has to study cycling accident issues in order to promote the public welfare. But the truth is that everybody reading this enjoys cycling and has no hesitation about encouraging you to ride. It's at least as safe as it is fun.