Question

Why did the United States want the Soviet Union to remove its nuclear

Answer 1

The problem  was the closeness of Cuba to US. If the Soviet Union had its nuclear weapons so close to the US it could fire them and they'd reach the US before US could react in any way (e.g. by shooting down the plane carrying it). Generally countries feel very uneasy about nuclear weapons controlled by an enemy (or potential enemy) so close to their borders.