The story
The name refers to the fact that many butterflies of this genus favor cabbages (among other plants) as host plants for their eggs.
Etymology from Wiktionary, CC BY-SA 4.0.
cabbage white
Today it means: Any of various largely white butterflies with dark markings in the family Pieridae, especially the species Pieris brassicae, Pieris canidia, and Pieris rapae. Full definition →