why did the colonists reach the conclusion that membership in the empire threatened their freedoms, rather than guaranteed them

By getting a membership in the empire it threatened their freedom, because the empire is slowly weakening their freedom. After the Seven Years' War, Britain government was in a huge debt. Due to the debt, government in London was trying to force colonies to share a cost of the empire. The colonies saw this as the government's plan to slowly decrease their freedom. Due to power the government has over them, there is no way of opposing them. Not only that, because of the debt, British government wanted to get more profit to repay their debt by a series measure. It mean they wanted colonies in America worked for them and their debt. In the end, the colonies decided getting a membership with the empire would only threaten their freedom, rather than guarantee it.