why did he keep saying "really bad eggs"?

It's a play on words. A "bad egg" is a phrase used to describe a black sheep or person of ill-repute - which a pirate very much fits. Pirates would often also eat eggs on board their vessels, but due to their lifestyle often be forced to eat "bad" (i.e off) eggs.

>>84063306
But if there's anything fresh on-board a ship it'd be the eggs and bacon, until they end up slaughtering the last chicken and run out of pigs.

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>>84062954
He did a lot of shopping at Greg's Kegs & Eggs