Why?

Because this would have PRECLUDED George Washington and the next 3-4 sitting Presidents of the country from being President.
That was already covered with the "Citizen at the time of adoption" clause inserted into the requirements.

The part I disagree is your explanation (and that of others) about what constitutes being a citizen.
I didn't say he wasn't a citizen. I said he isn't a natural born citizen. It's very clear if you read what the framers had in mind and reading the documents THEY USED TO DEFINE THE TERM, the natural born citizen clause has a VERY specific meaning. Two citizen Parents and born in a state or territory of the home country.

Their reasoning went to divided loyalties. A child of two citizens would not have extra-state loyalties.