The great critic Alfred Kazin sheds some light on this question in an essay used as an afterword in some editions of the novel. Kazin posits that this novel was intended to follow Twain's other Mississippi novel, The Adventures of Tom Sawyer.
Huckleberry Finn was inferred to be just a sequel toTom Sawyer.
Regarding the earlier book, Kazin quotes Twain as saying:
"Part of my plan has been to try to pleasantly remind adults of what they once were themselves, and of how they felt and thought and talked, and what queer enterprises they sometimes engaged in."
Though the subject of the story of the later novel became more serious than anything in the Tom Sawyer story, the intention was still to fulfill the goal of the quote above.
We can see this intention borne out with the appearance of Tom Sawyer at the end of Huck's story. When the story is poised to become truly serious, with Jim captured and enslaved, Tom Sawyer arrives full of antics, humor, and wit, effectively saving the novel from its serious impulses.
The above explanation offers, perhaps, the central reason that Twain chose to use a boy as his protagonist - his intention was to remind adults of what childhood was like.
Regarding the themes of the work, Huck Finn's age works in favor of an honest contemplation of the disconnections between accepted social norms and what is morally right in a given situation. Huck is in a place, developmentally, where he is divided between his moral instincts and his moral instruction.
As a child, Huck is involved in the process of establishing his personal moral code. This makes Huck Finn a good choice for the protagonist of a novel examining the morality of slavery (in a way) and the morality of loyalty which troubles the boy repeatedly.
Although he does not acknowledge it as such, it is Huck's development of a higher standard than that of contemporary mores that enables him to partially overcome the dictates of his conscience and act the part of a "nigger-stealer."