What was John Adams trying to prove when he agreed to defend the British soldiers in the Boston Massacre?

As American politics would later show, John Adams was a conservative. Despite the radical nature of American independence, Adams was not himself a radical, despite being a chief advocate for independence. Where someone like Thomas Jefferson would support the idea of a revolution every twenty years and watering the tree of liberty with the blood of tyrants, Adams was definitely a proponent of law and order. In conservative, aristocratic British eyes, all Americans who didn’t side with the king were radicals out to destroy society. Granted, there were a lot of radicals in Boston in the period leading up to the Boston Massacre, and men like Adams were fully willing to recognize them as such. Adams feared these radicals as much as the British did.
It is questionable whether or not the Americans involved in the Boston Massacre should be called patriots. They were not involved in a peaceful protest. They threw rocks and snowballs at the British troops, so the troops were certainly provoked into firing their weapons. The Boston Massacre was not a battle; it was a riot. This riot inflamed American radicals such as Paul Revere, who used the incident as a public relations tool to whip up even more hysteria against the British. The event, no doubt, made the king and his allies feel justified in their view of Americans as radicals. But by defending the British soldiers involved in the Boston Massacre, Adams showed both his American countrymen and the British establishment that America was not controlled by radicals. The American Revolution was going to be a revolution in favor of law and order. America was not and would not be subjected to mob rule.

John Adams had the utmost respect for the law, believing that even the British soldiers responsible for the deaths of five people deserved council and fair trials. Adams wanted the fledgling nation founded on the ideals of justice and equality. Regardless of their actions and their influence in the political environment of the American colonies, Adams was adamant that the soldiers be treated fairly. Adams's actions were brave in that he opened himself up to the scrutiny and resentment of the radical members of the revolution.
Adams also emphasized that revenge begot only more conflict. The colonies had long experienced exploitation at the hands of the British government. If the leaders of the American Revolution permitted the taking of revenge against the British, America would be thrown into an endless war founded on bitterness and spite.