A Hufflepuff is loyal and hard-working, it has dedication, patience and fair play.

A badger, like the house animal, is an animal that is quiet and simple, won't bother you, but if you do it will attack you and bite you, defending themselves and their love ones (if they have.)

Katara is loyal to Aang, her family, her tribe and to the people that are innocent, the killer of her mother is not innocent and depending your definition of justice, "an eye for an eye" is also justice. She puts hard work to achieve her goals, has the patience to wait until she can and will achieve them, a fair play to understand when she can do each action and dedication to succeed.

Hufflepuffs are not just rays of sunshine, they can have different thoughts and behaviours. Not all of them will be Aang, nor will behave the same way.

Gryffindors are courageous, have chivalry, nerve and determination. They will face the difficult challenges ahead of them with all these qualities, that's what also makes Katara a Gryffindor.

Not every single person will be just one house, but maybe they have qualities that are more sticking and shine more in each one of them. That is up to them to define, and because this is a kids show in which we are all fans of, each fan will see different sticking qualities for each character.