I don't know if you noticed that, but when they make bike lanes they don't cut them off the sidewalk, they cut them into the car lanes, either taking a lane out or making the existing lane very narrow. Unlike a cyclist, which you see once in a blue moon, the reduced lanes are there forever, you drive through them all the time. Does this explain the paradox to you?

I, for one, cycle and still oppose bike lanes - they don't make cycling much safer (a car can easily jump a curb and most of these don't even have a curb, just some paint and plastic bollards in the best case) but impede traffic for everyone. If you want to increase cycling adoption you will piss off much fewer people and be 1000% more efficient by reigning in bike theft instead of building these lanes.