I don't think he comes across as arrogant either, it's more a form of myopia about their own ideas. Both Bret and Eric talk a lot about science, and to some extent they fancy themselves scientists even though they don't work in academia (I know Bret works or worked for a uni but he doesn't publish). Now I'm not saying you can't do research outside academia, lots of companies do research that is released publicly and sometimes single individuals produce great results in isolation too. However, their self proclaimed reasons for being outside the system don't stand up to scrutiny.
Eric goes on Joe Rogan to talk about his grand unification theory for physics, but has some kind of persecution complex where he justifies not actually releasing his results in written form by suggesting that if he tried to publish them they would be rejected on the basis of being too radical, while simultaneously saying that his ideas would get stolen and someone else would claim the credit for them (this is my understanding based on various podcasts/talkshows). He has suggested that Ed Witten, who is arguably the greatest physics genius alive today, got the credit for an idea of his, but he has no receipts. He's also talked about him and Bret having Nobel worthy ideas, despite them both basically never having produced anything of substance. Bret has some similar thing where he once submitted a paper and it got trashed in review (this happens all the time!!), and he seems to base much of his understanding of peer review on this incident.
The thing is that they have reasonable criticisms of academia, of publishing and so on, but they are armchair analysts while purporting to be overlooked geniuses (Eric much more so than Bret). And again, I find their conversations on a lot of political issues enjoyable, it's just that sometimes they're sniffing their own farts a little too much.