The basic reason for this, of course, is that the delegates to the Congress thought that it was time for the colonies to become independent from Britain. So the better question is to ask why the delegates had come to believe this. Why did the Congress declare independence when the First Continental Congress had not?
I would point to three reasons:
- Britain had rejected the "Olive Branch Petition" that the Congress had adopted in 1775. This petition had restated the colonies' devotion to the King and had asked that he stop his government from mistreating them. By rejecting it, Britain was telling the colonies that they would not get what they saw as fair treatment.
- Thomas Paine's "Common Sense" had been published. This pushed many more colonists towards the idea that the colonies should be independent and that monarchy was a bad system.
- Finally, there was the war. The colonies and Britain had been at war for a bit more than a year by this time and attitudes had hardened on both sides.
For these reasons, the Second Continental Congress decided to adopt a declaration of independence.