Source? A Commoner has 1d8 hp compared to a cat's 1d4. A cat's AC is 2 higher, but a Commoner's attack modifier is 2 higher. If the Commoner has a club, they're dealing 1d8 damage instead of 1d4, but even without that it's the same damage. A cat can absolutely win if it gets lucky. After all, one in eight commoners have only one hitpoint, but reliably?

Also, I don't think the fight's really comparable, since at low levels randomness matters a lot more. A Commoner is equally likely to have 1 hitpoint as 8. An adult red dragon is 95% likely to have HP from 227 to 286. And likewise, when you're dealing damage, it would be a lot more consistent.

That said, while a cat can't reliably kill a commoner, a party of four cats definitely can, and going up against a large number of weak enemies is not good in general. Also, dragons just get a few abilities, and depending on the DM maybe a few spells that aren't that high level. Going up against human spellcasters is not a great idea.