The Battle of Bunker Hill, fought on June 17, 1775, is often considered a victory for the Continental Army primarily because the British army sustained heavy casualties. Although the battle was technically a British victory in that they took control of the Charlestown Peninsula, they suffered significant losses, with around 1,000 British soldiers killed or wounded compared to about 400 American casualties. This high cost for the British demonstrated that the Continental Army could stand up to the British forces, boosting morale and support for the American cause.
So, the correct reason would be: The British army sustained heavy casualties.