In Algebraic Topology, why do we want to localize spaces?

Question

I'm reading May's More Concise Algebraic Topology and the first half of the book seems to be written under the assumption that the reader has the motivation that we want to localize the underlying topological space when doing computations. Coming from reading his prior book, this seems like a lot more highly technical machinery with no goal in sight. Where does the motivation for topological localization come from?