Why is 'where' an adverb and not a pronoun?

A: Where are you going?
B: I am going to school.

Where took the place of school and something that takes the place of a noun is a pronoun. So, why isn't where a pronoun?

Answer

Where does not take the place of school, which is, as you say, a noun.

It takes the place of to school, which is a prepositional phrase acting in this sentence as an adverb of directive location a subject complementing to the verb go.

I am going [to school] → I am going [where] → [Where] are you going?

You may, if you like, consider where as an interrogative pro-adverbPP.