Hagrid is a flobberworm.
Possibly Hagrid is a flobberworm Animagus. The protagonists thought that he started having all the lessons on Flobberworms because he was worried that more students could be hurt after the Hippogriff incident, but in fact he was having financial troubles after the Malfoy family sued him, couldn't afford food, and so he used his Flobberworm form so that the students would unknowingly feed him lettuce.
Also, Harry protests about Draco's story that Crabbe was bitten by a Flobberworm because 'they don't even have teeth!'. It is canonical that Hagrid's rock cakes are hard enough to break one's teeth, so Hagrid having no or very few teeth seems fairly likely. COINCIDENCE?