Why is it that only natural-born citizens run for presidency?

It’s in the constitution. We’d have to amend the constitution otherwise.

I think their intention was foreigners could not come and “change” our country on a whim. The idea is that if you were born here, and lived here for a certain amount of time, you would have a better idea of what is best of the country.

it was to prevent a foreign power from becoming the highest authority. I believe it was feared that at the time of the founders a prince or king would be able to take control of the government and the clause was to prevent that. It doesn’t apply as much today, but its not an entirely poor idea either.