Why is the gullet so big?

Answer 1

This enables the frog to eat, in one gulp, food that is unwieldy (like earthworms), or nearly as wide as the frog's head. The frog is adapted for swallowing prey whole; there are no frog features for killing the prey first.

Answer 2

Most frogs have very wide mouths, or gullets, for a specific purpose. Since they do not have teeth, frogs must swallow their food whole. Thus, a larger mouth means they can eat larger food.