Why did New Englanders fight on 19 April 1775?
The British Army had sent troops to destroy weapons caches that had been stored by Americans in anticipation of an armed clash with the British. Word had gotten out and a group of "minutemen" attempted to stop the British. Shots were fired, and the result was the Revolutionary War.
The reasons, of course, are much more deeply rooted. Since the end of the Seven Years War (French and Indian War) Parliament had attempted to exercise increased control over the colonies, first by the Stamp Act, then the Declaratory Acts, asserting Parliament's right to legislate for the colonies. Following the Boston Tea Party, which was viewed with disfavor on both sides of the Atlantic, Parliament passed the "Coercive Acts," called the Intolerable Acts by the Colonists which essentially put much of New England under military rule and closed the port of Boston to all shipping until the tea was paid for. The various attempts by Parliament to control colonial affairs caused increasing resentment and finally led to armed resistance at Lexington and Concord.
April 19, 1775 was the date of the battles of Lexington and Concord, which were the first battles of the Revolutionary War.
The immediate cause of the fighting was the fact that the British army was marching to the countryside outside of Boston to find and capture or destroy caches of weapons that the patriots had been stockpiling at the town of Concord. When the patriots heard that this was going on, they gathered at Lexington and Concord to stop the British. The patriot resistance forced the British to retreat to Boston. These battles essentially started the Revolutionary War.