Why did the Second Continental Congress choose to declare its independence by breaking away from Great Britain?
The colonists were concerned that they were going to lose their freedoms in the colonies as British troops began to approach. The appointment of Washington as Commander of the army was in hopes of gaining support form the wealthy southerners to help finance the war.
At the time of their meeting, the Second Continental Congress understood that some steps needed to be taken in preparation for leaving England. While there was a Loyalist presence taken into account, the Second Continental Congress had understood that some trust had been breached, some level of transgression had been crossed. The Second Continental Congress had already seen the various acts and duties passsed against the Colonists and fully grasped that there was little in terms of the relationship between the new nation and the parent nation that could be salvaged. The selection of Washington as commander of troops, the printing of money, and the urging for all colonies to unify became steps that reflected the Congress' understanding that war was imminent and separation from Britain a reality.
Basically, the colonists decided that they had had enough of being ruled by the British.
The colonists had not reacted to well to the end of what was called the period of "benign neglect" when the British had pretty much left them alone to govern themselves. They came to feel that the liberties they had had during this time were theirs by right.
So then, when the British started to actually try to rule the colonies after the French and Indian War, the colonists were upset. They had gotten used to the freedom and did not want to have to actually obey any rules. After a decade or so of that, they declared independence.
From the end of the French and Indian War in 1763 to 1776 when independence was declared, colonists had amassed a long list of crimes they felt the King had committed. First among these was passing taxes on the colonies without their having any vote in Parliament (Taxation without representation). He also stationed troops in the private homes of citizens, even during time of peace when the cities were not endangered.
In Thomas Jefferson's Declaration of Independence, he pretty much told the King everything that had led the colonies to that point. He talked of the King getting rid of colonial legislatures any time they wouldn't do his bidding. He charged the King with making it as difficult as possible for the colonial government to even take care of their own smaller issues, without interference from the Governor.
In the end, it wasn't any one of these things that led the colonies to break away, but the slow and steady adding of one crime after another that led them to the breaking point.
The Second Continental Congress met in May 1775. By that time there was no appreciable change in policies of Great Britain in response to the Declaration of Rights adopted by the First Congress in October 1774. In the meantime fighting broke out between farmers of Massachusetts and English troops at Lexington and Concord. In view of these developments the Congress decided to take on the duties of the government, and to united the colonies in a war effort against Great Britain.
Congress issued a declaration setting forth the need to take up arms and the reasons for doing so in July 1775, and made a final, appeal to the king to set right matters without going to war. However Great Britain did not respond to this appeal and a war broke out. The Continental Congress then encouraged the colonies to set themselves up as states. Then on July 4, 1776, it adopted the Declaration of Independence.