Richard - to use your analogy, it is like Poland requiring
US citizens born in Poland to carry Polish passports to enter or stay in Poland. Even though they are now simply US citizens.
"No, no no - you still belong to us!"
From the US Embassy in Havana web site:
The Government of Cuba does not recognize the U.S. nationality of U.S. citizens who are Cuban-born. These individuals will be treated solely as Cuban citizens and may be subject to a range of restrictions and obligations. The Cuban government may require these individuals to enter and depart Cuba using a Cuban passport. Using a Cuban passport for this purpose does not jeopardize one's U.S. citizenship; however, such persons must use their U.S. passports to enter and depart the United States.