Born in 1451, Genoa [Italy], and regarded as "discoverer of the New World" Christopher Columbus is widely known for the four voyages in which Columbus played the part of hero, in being the means of bringing great material profit to Spain and to other European countries, and in opening up the Americas to European settlement.
coming back to the Title of the post "why did he sail westward" i came across this article which has provided some insight.

Christopher Columbus was an Italian from Genoa living in Portugal. Although in the fifteenth century most people still believed that the world was flat, others, including Columbus, had come to believe it was round. If this was so, he argued, a ship could sail around the globe and return to its original starting point.
Thus the shortest route to the spice Islands of the East Indies would by sailing Westwards. He sought support for his theory but it was rejected again and again. Finally, after years of disappointment, he gained the help of Ferdinand and Isabella, the king and queen of Spain.
In August 1492, three small ships set sail from Spain, their bows pointing westwards across the wide, unknown Atlantic. They were the Santa Maria, the Nina and the Pinta. On 12 October land was sighted. Columbus was convinced that it was an island off the coast of India. When other islands came into view he named them the ‘Indies’. His ‘mistake’ was nevertheless a vitally important event in the discovery and exploration of the west.
Hope that clears some doubts and it also brings us to the end of our history class.
Source - Inventions