In Columbus' time Egypt was under Muslim rule, and it wasn't practical for Europeans to travel via Egypt and the Red Sea to get to India. The Portuguese had discovered the route around Africa by 1488, but Columbus thought it would be easier and shorter to sail directly west across the Atlantic...because he thought the world was much smaller than it really is, and didn't know that there was a landmass in the way. In 1492, the Portugese had exclusive rights to trade with India by sailing Eastward, either around the Cape or by dealing with the islamic Middle East.
Columbus was working for the Spanish who were looking for a rival way to trade with the Indies.
So9
I don't think the Portuguese had exclusive rights in the 1400s. That was only crated in the 1500s when the Spanisha nd Portuguese asked the Pope to arbitrate. He drew a line on the globe and said that the Portuguese could control the lands to the east of the line -- that's why Brazil was Portuguese and the Phillipines spanish.