Let's counter his arguments: how often has a paper wallet leaked millions of customer addresses?
Not really a fair comparison. How could a paper do that?
Exactly, that's my point

Consider this scenario:
You said you have a printer without WIFI. Maybe you bought it with cash, maybe with a credit card that shows your real name. That information is stored somewhere on a server. The shop gets hacked and the data gets leaked. Does that make your product (the printer) worse? Would you stop using it and throw it away?
Everybody has a printer, nobody cares about it, and nobody is going to hit you on the head with a $5 wrench to ask you about your printer.
Too many mistakes have happened that have caused people to lose money by not making a proper backup of their private key, using bad software solutions that send change to a different address whose private key you don't have, etc. Instead of that use HD wallets and forget about single keys. Hardware wallets happen to be a good compromise between security and simplicity.
That's all true, but doesn't mean paper wallets can't be used in certain cases. In fact, it works just as well as it did 10 years ago, and that's the beauty of paper wallets: it will still work the same decades later.