You have touched on something very important when you ask about the theme and the characters in Big Red. Why? It is, in essence, a bildungsroman (or a coming-of-age novel) and, as such, has Danny’s coming-of-age as its prominent theme. This nicely ties into the idea that Danny and his father are the protagonist and the antagonist respectively.
As stated in the introduction, the theme of Big Red is Danny’s coming-of-age: Danny’s becoming an adult in the hunting world. Now, how is this idea of entrance into adulthood explored? First, the author (Kjelgaard) explores Danny’s relationship with his father. Later, the reader is exposed to Danny’s ability in regards to survival at Wintapi. Finally, Danny needs to be able to go beyond that Wintapi world and explore the new world presented by the character of Mr. Haggin.
It is the relationship between the protagonist and the antagonist in this story that is the most interesting. In regards to Danny being the protagonist, he is such simply because he is the main character of the story. In regards to Danny’s father being the antagonist, he is the antagonist because, even though he is much beloved, he is still the character that struggles against Danny’s desire to grow up (even though he is never in direct opposition to Danny). We can see this relationship struggle most graphically (in this eNotes educator’s opinion) in Danny’s reaction to the dog named Red. Before this point, Danny and his dad always work as a team, but after this point they are in opposition as to how to treat the hounds. Danny knows, by instinct, that Red should not be beaten. Danny has begun his new path. In what happens to Red, Danny wants accepts the responsibility fully, even though it was thousands of dollars that needed to be paid.
[It] was an unheard-of sum to one who knew triumph when he captured a seventy-five cent skunk or weasel pelt. [But now Danny has] cast off the old shackles [and knows that] if others could do big things, so could he.
In conclusion, it’s important to note that this is a perfect example of when an antagonist is not necessarily the “villain” or the “bad guy” in the story, but simply the character that stands up against Danny becoming an adult: the character that clings more to Danny’s past. In this way, Danny’s father clearly is the antagonist in the story, although still a loving father willing to teach his son all about hunting and wood lore and trapping.