Phillip has been raised to act like an entitled, privileged, and racist individual, and therefore thinks of himself as superior. Phillip thinks of black people as less worthy than he is.  Take the following quote that Phillip says to Timothy at one point.  

"You ugly black man! I won't do it! You're stupid, you can't even spell."

It's clear that Phillip believes that Timothy is incapable of teaching and helping Phillip because Timothy is black.  In Phillip's eyes, being black makes a person both dumb and ugly.  

Once on the cay, Timothy treats Phillip with respect even though Phillip doesn't do the same in return; however, Timothy doesn't grovel at Phillip's feet the way that Phillip might be used to seeing from an old, black man.  In fact, right after Phillip says the above quote, Timothy slaps Phillip for saying it.  The action shocks Phillip, and it serves as a turning point in their relationship.  Phillip is surprised at the developing relationship because, despite, the racial divide and vast age difference, Phillip begins to see Timothy as an equal.  By the end of that chapter, Phillip asks if the two of them can be friends. By the time that Timothy dies, their friendship is a strong and deep relationship.  

I didn't know what to say over the grave. I said, "thank you, Timothy," and then turned my face to the sky. I said, "Take care of him, God, he was good to me."