Why do some people say they will "eat their hat" when they make a
statement or make a promise?

The answer goes back a *long* way: eggs, dates, salt, saffron,
and veal are the main ingredients in an old and "tasty" (not
really) dish called "hattes." When someone wanted to give their
absolute assurance an agreement would be carried out, they would
often promise to do so or "eat hattes."

Somehow throughout time, the word "hattes" was misinterpreted and
people started to promise to "eat their hats."