Sokka is feeling disheartened because of the inevitable contrast he (and, let's admit it, we the audience as well) draws between himself and Aang, Katara, and Toph.
Measured against "Team Avatar's" incredible Element Benders, Sokka is merely an ornament or, at worst, a hindrance.
This is a feeling which is ALL PERVASIVE in our own society : a spirit-draining sense of strangling inadequacy.
Sokka is fortunate that he has friends who have experienced a great deal in their short lives and have become strong.
When they all encourage Sokka to seek out Piandao, the greatest sword master of the Fire Nation, they all speak from personal experience.
Words supported by personal experience hold weight.
The Student-Teacher relationship is one of the great themes of Anime, indeed, of all quest stories.
It is an fundamental need of human beings to grow, and, a fundamental need of human beings to be taught by those with more experience than themselves.
In Anime, this is an experience undergone by young heroes.
"Ah, how I envy the young protagonists of Anime. To have a teacher to train you and guide you into growing stronger than you knew you could be..."Piandao is an excellent master.
"...for me...and for so very many other young people (for so very many people), Anime is that teacher."
It was wonderful that the writers of the show gave Sokka a master who understood how unique Sokka is and saw that Sokka's unique approach to situations, could be turned into great strength (as Anime teaches that indeed, anything can).
The wisdom.
The patience.
The support.
Characteristics like these are what make the Master so important in the life of a Student.
Under the guidance of a true Master, a Student knows they can grow without fear of making mistakes, because a true Master understands,
"A mistake is simply a learning experience one does not recognize immediately. But, given time, a mistakes worth becomes apparent in the learning it imparts."
A Student flourishes under the hand of a true Master.
One of the great reasons why Anime is so pervasively popular is because of the forever repeated story of Students learning from Masters.
Our society is bursting with people seeking the same guidance.
It is a shame that Anime is tainted with economics and that so many people pay homage to their love of Anime through product purchase and limit their attachment to Anime to that and do not seek the deep meanings the creators of Anime seek to impart.
Anime must be recognized for what it is : not a money making enterprise, but an attempt to teach and guide a society which does not have the institutions, nor the traditions of providing the guidance, its members so avidly seek and so desperately need.
Sokka spends 2 days training with Piandao and emerges a promising young swordsman.
Fantasy?
I think not.
With the kind of recognition and understanding Piandao demonstrated to Sokka, coupled with Sokka's sense of keen need to gain a combat worthy skill, the sort of progress Sokka displayed is easily comprehensible.
Sokka needed to learn an ability which made him feel worthwhile.
That is what Master gives to a Student : the sense that the student is worthwhile and filled with promise.
"Ah...to have had that myself...well. I know what I have always needed, and I share it with everyone else, because : I think they need it too."
