Where We Get ‘Wolf Down’
The right choice is to say people wolfed down their food, as if they were eating like a ravenous wolf in the wild. According to the Oxford English Dictionary, wolf was first used this way in the book The Seven Sons of Mammon in 1862, where the line reads “[She] used to wolf her food with her fingers.”
Why ‘Woof Down’ Is an Eggcorn
To say someone woofed down a meal is a specific kind of error called an eggcorn, a term that was coined in 2003 by linguists on the website Language Log. They noticed that a woman had called an acorn an egg corn. On the Eggcorn Database site, they explain that what makes this something more than a misspelling is if you don’t know the spelling, eggcorn actually makes sense because an acorn is shaped like an egg and a kernel of corn can be a seed just like an acorn is a seed. Since this was the first example they had seen of this kind of error, they named the class of error an eggcorn.
Woofed down is an eggcorn because if you don’t know the spelling, woof makes sense because these days, you’re much more likely to see a hungry dog eating a meal than a hungry wolf, and you can imagine a dog gulping down a meal as if in a single woof.