Why did the Spanish explorers and the priest who came with the conquistadors think that it was their job to convert the native Americans into Christianity

Their interpataion on the Catholic religion is that it was their God given duty to spread the religion to every soul in existence.

During the time of Spanish colonization, explorers thought the new discovered lands could represent an opportunity to grow their economy and the economy of their country. For this to be possible, they had to interact with local people, something which eventually would turn into colonization.

And in this process, the Spanish explorers were accompanied by priests of the Catholic Church sent by the King, who considered it was his unifying and moral duty to make sure Christianity reached the New World. Through what they called missions, they preached their religion as well as their way of dressing, their customs and behavior.