Final answer:
King George III disagreed with the colonists because of the British view that colonies existed to support the motherland, with events like taxation without representation and military actions further estranging the colonists, leading to calls for independence and the American Revolutionary War.
Step-by-step explanation:
King George III didn't agree to the colonists' demands primarily due to a fundamental difference in perspective regarding the relationship between the colonies and Britain. The King and Parliament saw the colonies as subjects to British authority, meant to support the mother country even at the cost of their interests. Parliament’s 1775 Conciliatory Proposition, which Lord North presented, reaffirmed Parliament's right to legislate for the colonies, with the only concession that taxes would regulate trade and the proceeds would benefit the colonies, provided they contributed to their defense. This fell short of what the colonists desired— greater autonomy and the right to self-government.
Events such as the imposition of taxes without representation and the British response to colonial protests (such as the ones against the Stamp Act) reinforced the colonists' perception of an overbearing and unresponsive Crown. The colonists' vision of liberty and rights under the British constitution was incompatible with the reality of the restraints and taxes imposed by Parliament. This all culminated when the Second Continental Congress met in 1775, following conflicts at Lexington and Concord, choosing to prepare for war rather than wait for an insufficient response from the King.