There are at least three reasons that can be cited for this breakdown.
First, there was the fact that the countries that owned many colonies came out of the war much weaker than they had entered it. France and the United Kingdom, in particular, had substantial colonial empires but came out of the war in weakened conditions. This made it much harder for them to have the power and wealth needed to keep a hold on their colonies. (This was even harder for France which had essentially lost WWII and therefore had lost prestige among its subjects.)
Second, there was waning acceptance of colonialism. The colonized people were less accepting of being colonized, as can be seen in the movements led by people such as Gandhi in India and Ho Chi Minh in Vietnam. The United States, which had emerged as the leader of the free world, was also relatively opposed to the idea of colonialism. Both of these factors made it harder for countries such as Britain and France to hold their colonies.
Finally, there was the Cold War. The West needed to appeal to countries in the “Third World” so that those countries would not become communist. It was hard to do that when the West was seen as colonial oppressors. Therefore, there was pressure on Western countries to end their colonialism so that the West’s democratic form of government would be more appealing to the peoples of the Third World.