Unfortunately, as you say, peoples’ fears and demands are based on perception. I suspect that you can show them all the facts you like, but the perception is still that a lot of cyclists are jumping red lights, cycling on the pavement or going the wrong way down one-way streets.
This behaviour — which is more obviously and frequently bad than the average behaviour of cars, HGVs etc — makes *all* cyclists appear potentially dangerous. Although HGVs are statistically more dangerous to me when I’m a pedestrian I hardly ever see them doing anything obviously wrong and I know that, nearly all the time, they will stay on the road and obey the rules. They’re predictable.
As a some-time cyclist it saddens me whenever I see a cyclist jumping lights etc. It’s so *easy* to do this right and following the rules would help the cause of all cyclists. If the perception of cyclists was that they were predictable (as you’ve said before, they should think of themselves as vehicles, not pedestrians, and act accordingly) then people wouldn’t have this skewed view of how dangerous they think cyclists are.