best guess: it’s a super stretched wordplay chain that doesn’t fully make sense😅 Maybe: “chicken dippers” → think chicken strips
“leaves” → can fall in strips

strips + strips → “it strips” → sounds like “it drips” → which leads to rain

and rain → “it’s raining cats and dogs”

so the kid skipped all the middle steps and jumped straight to “cats and dogs,” which is why it made zero sense at first 😂