Why did columbus believe he had reach asia when he had acually traveled less than halfway there?

Because at the time Europeans didn't know North America was there. No one before 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 southeast. 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.