Describe the reasons why each group fought in the american revolution

There were two main groups of people, not counting the British empire. Among the Americans, there were loyalists and there were patriots.

The British empire believed that it was their right to control the colonies since they were a colony of Britain and in order to ensure their mercantilist policies were making them more powerful they needed to have the colonies under pressure and under control and put down any rebellion or anything similar that might have occurred. 

The loyalists were people who didn't want the colonies to become indipendent. They worked closely with the Empire and the change in power would not be good for them since they were often either governors or rich merchants or anything similar that put them in the position of power in the colonies.

The patriots were those who wanted to become independent. They believed that the British empire was exploiting the colonies and that the colonies should have sovereignty over their own territory and choose things like taxes and wars and similar things and not just be involved in anything bad that Britain decided to do.