There is “misinformation”, saying something untrue, then there is straight up spreading lies you know are untrue (Duke rape case), trying to cover it up when exposed and doing it multiple times.
I think the 2nd can permanently destroy credibility.
You can see him using motivated reasoning to defend the talking point he was trying to advance -- a talking point that itself has an obvious agenda behind it.
Rogan has a long history of false vaccine claims on his show, presented both by him and his guests:
https://www.rollingstone.com/culture/culture-news/covid-misi...
He'll surely challenge a guest when he thinks they're wrong, it's his own mistruths and the ones he ignores that are at issue here.