The answer above covers it pretty well. Here are a couple of other points to consider. The French and Indian War lasted for nine years, and was expensive to the tune of $15,000,000. The King and the British people wanted it done and over with. So by defeating the French and negotiating the Treaty of Paris, that took care of one enemy, but the tribes on the frontier who had fought alongside the French had also been armed by them, and remained a threat.
So the King wanted to buy them off with guarantees of land, west of the Appalachians. The Proclamation was that guarantee. Most of the people living there were poor, former indentured servants and late arrivals to the colonies, who owned no slaves and worked small family farms, often living off the land as frontiersmen. These were Scots-Irish, and they had no love for the King.
So they ignored his order and settled west of the line anyway, causing more tension with the native tribes there.