Why is Odysseus the protagonist of the Odyssey?If he does not appear until chapter 5, how can he be the protagonist?
The answer to this question has to do with the definition of "protagonist." What you're really asking is "Why is Odysseus the character that we would like to see triumphant in the story?" In this context, it is easier to make sense of.
It doesn't matter that Odysseus doesn't come into the story until the 5th chapter. It's not like the first 4 are a different story...though he is not present directly the content of those chapters sets the stage by introducing the reader to other characters and the details of the setting.
So, in a nutshell, Odysseus is the protagonist of the Odyssey because he is the individual that we want to reach his goals, and he is the "main" protagonist because the story revolves around his life and situation.