According to the Junior Jedi Knights series of novels about the Skywalker/Solo children, Ikrit was trained by Yoda centuries before the events in any of the movies, because in the Star Wars universe muppets have a longer lifespan than most modern nations. After somehow passing Jedi School, Ikrit went into exile for 400 years, presumably because someone locked him in a garage without a cat door, before Han's batshit crazy child found him and eagerly accepted the opportunity to be trained by the mystical rodent.
Why He Doesn't Belong:
He could either be running from Darth Vader or a Pokemon Master.
Probably Ikrit's most glaring deficiency would be the lack of opposable thumbs, something a Jedi would find pretty crucial in the operation of a lightsaber. Even Yoda could switch one on and pump up the jams like House Party 3, so as far as we're concerned Ikrit has no excuse. Also, we just can' t picture something that looks this much like a Care Bear going toe to toe against somebody like Darth Vader.