Why was Columbus sailing to the west?

He was trying to reach China and India (the Indies). Knowing that the Earth was round, he knew that he could reach the East by going west around the planet. But his cartographers has vastly underestimated the circumference of the Earth and the longitude of China. His arduously long voyage gave him a better idea of the vast distances involved.
Still, when Columbus encountered the red-skinned natives of the Caribbean, he thought he had reached southeast Asia, and called the natives "Indians."