They needed the public to be behind them if their movement was going to work. By making the slavery parallel, they moved colonists to action. Colonists would have been irate at the concept that they, the superior white people could be in the same position as the African slaves they believed were inferior. In the end, this is an effective theoretical device for two reasons, it was relevant to every colonist and it elicited a strong negative reaction.
2) It was a risky move, but also a calculated one. The Sons of Liberty needed to push people into joining their cause. The most effective way to do this was to make them emotionally invested. They had to feel like they were being wronged, like they were the victim. They had to care. To make them care, the Sons needed to keep pushing and make a big negative statement about how Britain was treating the colonists. Drawing the parallel to slavery did just this. Nobody wanted to be a slave because it lowered their