The story
Supposedly uses the American English and British English pronunciations of the word potato, by analogy of tomato (see tomayto, tomahto). Unlike tomato, only the former pronunciation is used in either American or British English. Allusion to George Gershwin's song "Let's Call the Whole Thing Off": "You like potato (/pəˈteɪtoʊ/) and I like potato (/pəˈtɑːtoʊ/)".
Etymology from Wiktionary, CC BY-SA 4.0.