There's that Yoda explicitly says "Confer on you, the level of Jedi Knight the Coucil does. But agree on you taking this boy as your Padawan learner, I do not.... Agree, the council does. Your apprentice, young Skywalker will be." So they elevated him to Knight and gave him a Padawan. Knights are good enough to teach. I think of it like a grad student teaching undergrads, or an adjunct professor instead of one who has tenure.
Oh, a couple of other things: No. No, they do not.
And finally, Season 2, Episode 11 is my fave. Excited for you to get to that one.
They do cover that in the movie pilot, though; the council hopes that having a Padawan (especially an older, headstrong one) will force him to be more mindful of his own shortcomings.