Astral Projection stuff is something completely new, that she randomly obtained without it really being explained. So I don't see why that is being used as proof. And as far as everything else, while I agree fighting doesn't = master air bending, we haven't been shown anything else to indicate she is ready for the Tattoos.
That said, if you choose to believe she is, then Tenzin is just being a stubborn fool again. So either way you look at this, it's not a very good plot point (someone looks bad here).
Edit: to be clear I really liked episode 6 and thought 7 was fine. I didn't hate anything, just some small complaints (and most of these complaints stem from larger issues I had ). Episode 7s ending was really incredible. And the Tenzin stuff isn't bad in terms of the episode. I just have bigger issues with him that made aspects of this episode not as enjoyable for me personally.
The astral projection stuff, unfortunately, is a hold-over from Book 2 which was quite messy. They definitely missed the opportunity to show how she developed her "spirity powers".
I just can't help but love grumpy, stubborn Tenzin. It's made even better with his interactions with Bumi. I find it endearing. <3
i want P'Li to fry eggs with her mind
Wouldn't the eggs just explode?
That's one of the weakness of the combustion thing. Other than aiming you don't have much control over it.