Question

One of the reasons Spain spread Christianity in the Americas was to gain favor with

Answer 1

Spain would want to gain favour with the pope.

The pope was a powerful figure, as his blessing was taken to mean also God's blessing, so people didn't dare to go against it, and treated it as a law. So if the pope was supporting Spain, he could tell other rulers to help Spain militarity - this was one of the ways in which having the Pope's support mattered.