Yes, yes, hypocritical, etc, but really I had thought the interpretation was was one had to be born on some sort of US soil, a military base or embassy, etc. Not, born in another country, live their for years, etc.
The requirement is that they be a "natural-born citizen," meaning they need to be a citizen at birth and, thus, have never been an alien. That means they were either born on US soil, or are the child of US citizens.
The idea that they need to be on US soil is historically absurd. Expansion into the western regions of the continent were significant at the time, and far
outpaced the rate at which the government was including that land in their territorial boundaries (the government often being intentionally restrictive so they didn't reignite the French and Indian War conflicts). They also didn't wish to extend their territory too arbitrarily outward, because they didn't want to have to deal with the repercussions of native citizens (which they later addressed by... not affording them the rights of citizenship, while still considering them citizens under their domain).
How could that be though?
Scheduling births is like scheduling the weather. If an American woman happens to be on foreign soil when the babe decides to drop out we can't simply deny the kid citizenship.
Or, what if an American woman is having lunch at the french embassy with a friend when she has her baby. Would or could the kid be French?
If you want to stretch the idea, it's not TOO weird, barring the fact that the US was tiny at the time relative to the spread of its own citizens noted above. If a woman was sailing to a foreign nation, she probably wouldn't be coming back for some time. And it might be held that her child would be culturally French (or whatever) by the time they returned.
As for the reason for it, it's because the US was extremely insular in the early years after the revolution. The leading party was wary of the French influence on the Democratic-Republican rivals, and the Democratic-Republicans were deeply concerned by the heavy English influence on the Whigs. Culture war led to an anti-foreigner agreement from both parties (restricted to the other influence, but unified in a general legislative compromise).