What would cause my rabbit not to be able to chew a small carrot?

Sounds like your rabbits teeth are overgrown. A vet will be able to trim them, and he'll be back to normal.

Just a note, unless a rabbit is given the proper tools, food, and treats, to grind his teeth down, the teeth will grow, and can actually cause your rabbit to die.

A rabbits teeth grow constantly, for their entire life.

Right now a visit to the vet is a must. After that, purchase a grinding stone, timothy hay, and other grinding tools to keep your rabbit in check.

This is due to diet, and lack of materials. Please read up on proper rabbit care.

Good luck. :)