The sensational stories, as mentioned, certainly serve as an exacerbating backdrop to the hostility, but it has always felt to me like the root is in a misplaced sense of ownership: the idea that the road is for cars.
We're taught as children to cross safely - to wait for breaks in traffic, to push the button that temporarily halts the flow of traffic, to wait for the authority figure to hold up a sign and make it safe for us. The roads are full of cars - which, at a basic face-value level, makes it appear that the road is for cars - and we're told, from the outset - not to venture onto them. That we need special permission to enter the car's territory. The fact that non-car occupants of the road might have right-of-way is treated as a QI-esque "did you know?" curiosity.
That cars own the road is an easy assumption to make.
So the driver feels like they're doing the right thing, using the vehicle that belongs there. A human-powered vehicle doesn't belong. It's in the way. Everybody knows roads are for cars, so what the hell does this human-powered thing think it's doing? It should get out of my way, because everyone knows it is my way. I'm right, they're wrong. They're not making room for me, even though we both know they have to. And that's just...that's just rude. If someone is openly rude to me, I don't have to tolerate it - it's perfectly understandable that I should yell at them. I'm not being aggressive, I'm retaliating to this provocation by an interloper.
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Very obviously, the driver is wrong. But the whole culture of road-use has funneled them into that wrongness. Not an excuse, I hasten to add. But, without sustained blanket public information to tell them plainly that things are not as they think, that the hierarchy does not have the car at the top, well, it does seem to be an inevitability.