Alexander Hamilton opposed adding a Bill of Rights to the Constitution primarily because he believed that it could limit individual rights. His argument was that by listing specific rights, it might imply that any rights not listed were not protected, potentially leading to a misunderstanding that those unlisted rights were not guaranteed. Hamilton expressed this concern in Federalist No. 84, where he argued that the Constitution itself was a Bill of Rights, as it limited the government's powers and defined what the government could do.
To summarize, the correct reason Hamilton opposed a Bill of Rights was that he was afraid it would actually limit individuals' rights by not listing them all.