I'm a foreign born American. I can understand the reason for limiting our nation's two highest offices to native born Americans was and continues to be a valid one. Whatever one's personal desires are, they must take a backseat to the greater good of the country. Which is why the so-called "Arnold" Amendment is destined to go nowhere.
The Framer's wrote an exception that was intended to permit Alexander Hamilton to run for president eventually. Section 1 of Article I provides: "No Person except a natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution, shall be eligible to the Office of the President;"
Hamilton was born on the British island of Nevis. He was Washington's closest aid and first secretary of the Treasury. He was Jefferson's most bitter rival because he was a manager, a pragmatist, a capitalist (with a bit of industrial policy), and a New Yorker--all of the can-do things that Jefferson lacked in his world of theory.
Two of the greatest developments for the United States in its early years were that (1) Jefferson was fortunately in France during the Constitutional Convention and thus had little or no impact on making the document wacky, and (2) the country never had the benefit of Hamilton's presidency because Aaron Burr killed him in a duel.