If Catholic Christianity or Catholicism originated in Europe, what might explain why South America and Europe are both majority Catholic?

They are so because of colonization.

Explanation:

South America was colonized in whole by nations that were strongly catholic.

This is because Spain and Portugal, who were the prime colonizers in the region wanted to spread their culture there as far as possible and their religion was integral to this.

So most of the natives were made to convert to the religion of the colonizer.

This is why the South american regions are all catholic now like Spain and Portugal which have remained catholic too.