You said that we all share a fear of traffic. I pointed out that that isn't true - for instance I'm not afraid of traffic. I've not done as much riding as I'd like recently, but when I do it's usually in London and rural England. On the other hand I've been unafraid of traffic whether I'm riding on my usual roads or others, at all times of the day or night.
Three observations. First, when I learned that most drivers really don't want to hurt you I started enjoying my riding much more. Second, my observation is that people who report being afraid of traffic report far more near misses and crashes (see post above). So I suspect there's a bit of a distorted perception.
Third, and most importantly in the context of new rider encouragement, telling everyone how unpleasant and dangerous your pastime or mode of transport is isn't the best way of getting new people to do it - especially people who might be risk averse.
Of all the risks that might endanger a cyclist, cars and motorists are not very high on my list. My biggest concerns is that of taking a spill from poor road surfaces (gravel, -ve camber, black ice, pot holes), miss reading corners, clipless pedals etc. Have had a few near-misses, but they were all misses which may make you a bit irate, but in reality did not harm me. Experience on the road and learning how to read traffic flow is the best preventative action. In over 50 years, which includes commuting into London in the days when cycle/bus lanes did not exist, I've only had one incident which included a car, although the latter one was a serious one, but have had more than a dozen of those "minor" spills and some of these resulted in broken bones.
Black ice is currently no 1 on my risk list
But nothing ever puts me off from getting back out there.