That authority is granted by the North Carolina State Constitution.
NORTH CAROLINA STATE CONSTITUTION
ARTICLE VII. LOCAL GOVERNMENT
SECTION 1. General Assembly to provide for local government.
"The General Assembly shall provide for the organization and government and the fixing of boundaries of counties, cities and towns, and other governmental subdivisions, and, except as otherwise prohibited by this Constitution, may give such powers and duties to counties, cities and towns, and other governmental subdivisions as it may deem advisable."In fact, a neighborhood recently annexed into the City of Asheville, Biltmore Lake, was repealed by legislative fiat. Here's the local bill that made that possible:
And that's how local government works.
The Process of Annexation
City of Asheville
Annexation by a city or town must follow a specific procedure and must insure that urban services are provided to the areas to be annexed in a timely fashion and at a level substantially similar to that provided to other areas within the city or town.