Just to be clear, I don't think that is a valid argument. We, the drivers, are wrong. Most of us won't accept we're wrong because we're stubborn and few of us will admit the real reason because it'll show how wrong we are.
It boils down to incompatibility of bicycle with the rest of current road users. Bicycle is incompatible with pedestrian traffic, everyone understands that. And yet we do insist that it should be part of motorised traffic. It shouldn't. Purely as a method of locomotion it will never behave predictably and safely enough to fit with motorised traffic.
Unlike motorbikes, bicycle doesn't have speed, low center of mavity and does not move along sustainable, predictable path to guarantee safety of the "driver". I can overtake other cars in city traffic with 10mph speed difference between us and 30-50cm between our mirrors. I can overtake motorcyclist in city traffic with 10mph speed difference and 30-50cm between our mirrors and be sure nothing happens to him. I can not safely overtake cyclist with 30-50cm of the road to spare. And I simply do not have any more road to offer them for safety. Not in London. Not in most places in UK. It's not that I, as a motorised commuter don't want to. There is simply no way to do this.
And it can just slow motor traffic down. You can't just have chain of cars tailing in second gear behind someone moving at 10 mph. We understood it once, which is why we banned slow harvesting vehicles and tractors form public roads in rush hour. We don't let pedestrians walk down motorways, for the same reason. But we now insist on road traffic entertaining small minority of cyclists holding up and endangering lives all around major arteries of capital (and now Westway/A40 towards Oxford is being prepped for cycle lanes) at the massive cost to time, safety and air pollution.
I want cyclists to be able to ef around capital all they want, but this cannot be always one way ticket. I cannot guarantee their safety because it is them who create this lack of safety. Not me. I cannot be automatically responsible for the things they do. And they are not compatible with motorised traffic. And they do not want to be. They want to be jumping lights. They want to be squeezing between cars. They want to undertake. And they do not want to follow the same rules, safety measures and behaviour as the rest of the traffic. Make them their own separate pathways.
And it does not have to be that way. Cycle lanes do not have to be part of motor traffic roads. We could just sacrifice few small roads in city, pedestrianise them with separate cycle lanes. Build them perspex tunnels along rivers. Crossing ramps and separate paths through parks. We don't mix cars with trains, underground with boats. Let's not mix bicycles with cars and motorbikes. Sounds harsh, but you know it's the only sensible way out of this situation.
I actually did some lessons and a test to cycle on the roads when I was a kid. I have no idea if it's mandatory, but it's something I did in an after school thing.
One of the girls in office next to us cycles to work for several years but she's partially colour blind. She can only see yellow in addition to black and white. There is nothing preventing her from using bicycle on public roads at the moment. My heart cries for her, but surely that's not motherloving right, is it?