He probably means those famous paper wallet generating websites. If you make your own paper wallets yourself using a trusted wallet like electrum or core, I don't think there is any harm doing so. A paper wallet is just a paper which keeps your private keys and nothing else. You can write down your private keys on a random piece of paper and it will become a paper wallet. That's how I imagine a paper wallet whenever I hear it.
It would be better if there was specialized software that you can download and install that is just for generating a paper wallet.
It is quite surprising that nobody has attempted to make such a program yet, forcing everyone to rely on these unsafe websites. For the record, even legit websites like bitaddress.org are not safe to generate private keys on, because the HTML can be manipulated by an Inspect Element or something like that.
Paper is easily destroyed by the likes of water and rats though. Better would be inside a text file on a CD-R in a storage sleeve - already rat-proof, not really waterproof but that can be solved by putting the sleeve in a safe or something like that - and, unlike paper wallets, are easily destroyed when they are no longer needed. Now there isn't really a use case for destroying paper wallets besides protecting your privacy by hiding the addresses you used, but you'd need to buy an expensive paper shredder to do the equivalent for paper wallets. A CD can be destroyed cheaply.