Whenever you're reading a literary work, remember that not everything is a symbol or is to be taken as significant. It is a common mistake for both teachers and students to "read into" a text much more than the author ever intended. My question: Did Harper Lee ever state (orally or written) that she meant something by this particular description? If not, my answer, yours or your teacher's is just sheer speculation.
This said, it's nevertheless a fact that certain words carry both a denotation (literal meaning) and connotation (associative suggestion). The word "feathery" means "like a feather" (denotation); it suggests thinned out or wispy hair, much as in a very young child or old person. Describing Boo in this way could be a good way to make the point that Boo had spent most all his life cooped up in the Radley house and was now showing signs of growing old. His fragile innocence and extreme vulnerability also come across in Harper Lee's description, far from the raw squirrel-eating, drooling maniac he was cracked out to be at the beginning of the story.