Oh, I can explain it pretty easily.
I listened to rush a fair bit. It started because he was my father's favorite broadcaster when I was a child and it continued on into my early 20s.
One thing that rush did in an excellent way was making you feel like you were smart, special, and inherently in the right by listening to him and supporting him. It was much like listening to a preacher if you have any sort of religious upbringing (which I did).
And while rush did primarily work at demonizing people, he often demonized "the right people". Primarily democrats. He also knew his audience well and did a great job of hyping the "us v them" notions. He knew a lot of his audience was rural, for example, so he'd spend a good amount of time talking about how much more wise country folk and truck drivers were vs people that live and work in the cities. He had an answer for why things were bad, it's the unions, feminists, democrats, muslims, big government, clinton, obama, socialists, communists, etc. He could always give a reason why something was bad and would expressly tell his audience "You don't need to look into this, because listening to me will make you smarter than any college professor". He trained his audience to explicitly trust him.
And, frankly, he could be both funny and entertaining to listen to. He'd take in calls and had a good delay that allowed him to only air the dumbest liberals on the planet. He was further not afraid of simply hanging up on them and calling them morons if they ever started to get the upper hand in a conversation.
It also helped that in terms of broadcasting, he was infinitely accessible. I, in rural idaho, had really easy access to him because radio stations carried him. AFAIK, the most left wing broadcast in idaho in my youth was NPR. Which, today I find laughable that I thought of it as "leftist".