Why would both the British and the colonists have wanted to control the Charlestown peninsula

The Americans, having heard the words in the British plan to strengthen the Charlestown Peninsula, decided to get to the peninsula first, strengthen it and pose a sufficient threat to force the British to leave Boston. On June 16, 1775, under the leadership of General Putnam and Colonel Prescott, the Americans occupied Charlestown on the peninsula with instructions on building defensive positions on Bunker Hill.

The redoubt, a small and usually temporary defensive fortification, was built on a hill, probably due to its greater proximity to Boston compared to Bunker Hill. The next morning, June 17, the British were surprised to see the rebel fortifications on the hill and set off to return the peninsula. As a result, the conflict was called Battle Bunker Hill, because this is where Prescott was originally supposed to, and was ordered to build fortifications. In addition, some people considered Hill rocks to be part of Bunker Hill, while others called it Charlestown Hill.