What's his reasoning behind that?
I think his rationale is that there has been a huge explosion of passive investing over the last 2 years. It is now at a point where most people (even marks like myself) say do passive investing. For a contrarian investor like Burry, this sort of sentiment is often the exact moment where things tend to be ready for a fall.
For what it's worth, I do see some rationale to it. Passive investing inflows have undoubtedly contributed to the stock market's rise. When people say we have seen the end of a bear market, we are not near that. We are only near it when pension funds avoid buying equities because they feel stocks are a bad investment. We are not at that point.
However at it's core, I don't agree with him. ETF's are not singular companies, or commodities like a home. They are derivatives (I.e they derive their price off a secondary thing, normally the S&P/Down Jones index). So people buying loads of them does not rocket the price in the same way. It's not to say it doesn't contribute, but it's not as dramatic. Likewise, they are no more expensive than the stocks in that index, so avoid ETF's which give broad coverage, to buy the same singular stocks in those indexes which are expensive/overbought is not really solving the problem. If anything it's just exposing people to greater risk.
I fully appreciate this is not what Burry does. He goes for unique, anomalous bets, like prisons, or someone like QRTEA, but most people would simply not do that, or want to do that.
I would also acknowledge index's, particularly American ones are expensive currently. But if people are starting out, I would advise they dollar cost average in, chop their money up onto 12/24 parts, and buy the same amount each month. If you do that, and have a longer time horizon, you should do ok in the end.