Eric claims that he, his brother, and his wife have all made important scientific discoveries in theoretical physics, biology and economics which were either ignored or stolen by the establishment. Most of the episode is about his brother who found that selective breeding practises in laboratory mice produced animals that due to long telomeres, were more likely to get cancer and were better at repairing tissue damage. The implication being that mice are not good animal models for medical research. One of the world's leading researchers on telomeres, who won a novel prize for the work allegedly helped Bret Weinstein in the initial stages of this telomere study, then tried to block publication of Bret's article through peer review suppression (which didn't work, the article was published anyway), and also published on the same data, interpreting it differently but not acknowledging Bret at all.
I can tell you that the idea that mice are not great models of disease is hardly a groundbreaking realisation. Eric and to a lesser extent Bret try to inflate the significance of this discovery as much as possible, which gets quite cringeworthy at many points.
Eric berates scientific peer review as a highly flawed system, which obstructs science and stops people with good ideas that aren't part of the establishment from making important contributions. This fits into his broader narrative that the boomer generation holds all the power and aren't interested in letting anyone else thrive. This is hardly anything new. His personal example doesn't actually involve peer review per se. He says he discovered something important in theoretical physics as a graduate student, but some senior physicist brushed him off, so he didn't work on it or publish anything. Some time later Ed Whitten apparently came up with the same thing, which was lauded as a brilliant discovery. I mean, doesn't everyone have a story like this? Science just isn't a system which rewards people commensurate to their cleverness. Many clever people don't do science for this reason I suspect, going off to be chess masters or quant traders (which is fine).
Of course you could say to Eric, well, you shouldn't have been deterred and published your work anyway. He tries to see off this quite legitimate challenge by saying that because of peer review, there was no point in trying to do this. This is a fairly circular argument. The Portal is a very interesting podcast and I will keep listening, but hopefully there aren't too many more self-entitled diatribes like this one.