Huck has grown up in a supposedly uncivilized, marginal way with his drunken father until he runs off and is adopted by the Widow Douglas. On a literal level, Huck is unused to the restrictions and expectations of nineteenth century middle-class life. He simply finds the clothing, manners, social norms,...
and schedules of the Douglas household oppressive, and, on some level, weird and incomprehensible.
His sense of being uncivilized, however, goes deeper than this. Though he blames himself for his discomfort and inability to fit in, deciding he is not going to go the heaven described by the Widow Douglas and Miss Watson, it is actually not he who is the problem. An honest and forthright person, Huck is, even if he doesn't fully realize it, uncomfortable with the deep-seated hypocrisy of Southern society. He is taught an upside down morality in this household, where one can be a slave owner and at the same time a good Christian headed for heaven. He learns about Christian mercy and morality from the Widow Douglas and Miss Watson and yet witnesses them forcing the tired slaves to pray at night. His thoughts about the world he has been drawn in to may be inchoate, but some innately good and innocent quality in him rejects it.
Huck, therefore, not only flees the superficial restraints of "sivilized" society such as uncomfortable clothing, he instinctively flees a society that wants to train him to be similarly hypocritical.