The version of this joke I know, told by
Irish comedian Dave Allen, is slightly different, and I think a little funnier (no offense, wharfinger!).
In this version, the wide-mouthed frog is talking to all the animals, because he's looking for help, because the wide-mouthed frog is almost extinct. As Allen tells the story, he stretches his mouth wide with his index fingers, which makes for a funny voice. He asks each of the other animals if they can help him, until he comes to the alligator. Or ocelot. Whatever.
The wide-mouthed frog says "We wide-mouthed frogs are in danger of becoming extinct! Won't you please, please help me?"
And the predator says, "I like to eat wide-mouthed frogs."
And the wide-mouthed frog purses his mouth and says "you don't see many of them around these days, do you?"
I just like the suggestion that the wide-mouthed frogs aren't actualy extinct, just in hiding.
Chattering Magpie's version is better still. Dave Allen's version pretty much requires the WMF to confess its species to the predator and then turn around and deny it, while Magpie's can be a little more subtle. I'm really curious about the evolution of this joke and others. Lots of people go around repeating jokes in paraphrase without thinking about what makes them funny, and it turns into something of a game of telephone. Only the ruthless culling of the least fit, least funny versions keeps people from going around saying "So there's this frog talking to this alligator and suddenly he squinches his mouth up real small. Ha! Ha!"
However:
"Humor can be dissected, as a frog can, but the thing dies in the process
and the innards are discouraging to any but the pure scientific mind. "
-- E. B. White
Interestingly, this quote seems to mutate as much as the wide-mouthed-frog joke. I found three different phrasings in a quick Googling.