Why did Columbus believe he had reached Asia when he had actually traveled less than halfway there?

He believed the world was much smaller than it really was

Because at the time Europeans didn't know North America was there. No one had traveled to Asia by sailing west from Europe, so they didn't know how long it would take. Previously, the only way to get to Asia from Europe was by traveling east or southwest. But Columbus thought he might be able to sail west from Europe to reach Asia. That's what he set out to do but he bumped into North America instead.