In theater, and it can also apply to literature, there are several dimensions of satire. Satire, as described in the 14th century, is a work of art intended to ridicule something.
The purpose of this ridicule is not just to mock, but also to aim to reform. Therefore, Twain's use of satire was to bring up the redeemable traits of his character, Huckleberry Finn, and not just laugh or mock them, but also to use them as a form of cautionary tale for those who attempt to engage in similar behaviors. However, Twain was clearly up to something else. He wanted to infuse the excitement of youth onto the reader using this conduit.
Twain lived in the 19th century, which was a time when educational reform, as we know it, was nonexistent. Children were seldom seen as what they were, and the fields of educational psychology, sociology, social work, et al were also unheard of. Hence, the mentality of the time would be: Why not mock teenagers and expose them for the fools they are sometimes?
In comes bitter satire. Bitter satire is also known as Juvenalian, (for Juvenal, as Horatian is for Horatio). Interestingly, the term "juvenile" comes also from that root word family, meaning "youthful". This kind of satire is used as a cautionary type of tale, intended entirely to judge and react with indignation at the things portrayed in it.
All this being said, let's stop for a moment and analyze. Why would Mark Twain (of all people) want to indoctrinate and caution society, when he is a master of joke and giggle? His own pen name is a satire!
The answer is that he used bitter satire as his selected sub genre to bring out the comedy of his work with more punch. His purpose to write was to entertain, and not dictate anything. He used bitter satire as a mechanism to infuse his humor, not intending to judge or caution anyone.
This selection of genre is actually quite clever . Using a judgmental, cautionary style would have served the same purpose as the modern day "mockumentary", which is intended to sound serious, but is actually quite trivial. That is what the bitter satire is, and why Twain used it. After all, he did not title his novel The life and time of Huck Finn but, instead, he titled the novel The ADVENTURES of Huckleberry Finn.
Twain was up to something; he wanted to tell a tale of a bold teenager undergoing amazing circumstances. He would have wanted to be Huck, himself. This is why he told his story the way that he did using bitter satire.