The gang are weary of your presence.

That's putting it lightly, most don't trust you, Katara openly hates you, Aang is willing to give you a chance though. You've tainted your hands when aiding Azula, yet now you have defected from the Crown Princess to help the Avatar and bring down Fire Lord Ozai.

You are a master firebender, the most suitable candidate to teach Aang the final element and complete his training - Fire. He is nervous about it, both about you and fire itself, the Avatar could not learn firebending before, he could not master it, could not control himself! And you are... well, you. But now it is obvious that Aang needs to learn, and who's a better teacher than you?

"I am ready, let's begin."

The Avatar's words were heavy.

This can be very-very bad - an internal rational voice kept saying (and the external voice of Katara said the same thing), but no, Aang is an air nomad, they forgive, they give second chances... just have to give one to you too.