I'd say that no small part of the rage comes from fear. If I'm driving next to a cyclist that breaks the rules, I have to immediately become hypervigilant and pay a disproprortionate amount of attention to this cyclist and their behavior. It's my responsibility to pay that attention, though, because if I don't, I'm risking seriously injuring or even killing that person.

Humans on wheels are extremely vulnerable. Frankly, a lot of cyclist behavior I see when I'm driving involves a pretty low level of vigilance - it certainly doesn't scale with the amount of danger they're facing. I don't mean to sound overdramatic here, but if I break a driving rule like forgetting to signal, and I get rear-ended, that sucks balls for me, but there was virtually no chance of me being killed (or killing somebody), assuming a city environment. Regardless of legal implications, nobody wants that on their hands, and it's easy to see how worrying about it would get anybody heated.