Why did the British fight settlers that wanted a new life in America?

Because they refused to pay taxes to the (English) Crown.

At that time white British people were considered to be superior to all other races, so they mistreated everyone else.

They didn't.

They fought "traitors" who took up arms against the Crown.

The British wanted control of all the land and natural resources and all trade so Great Britain could could fiil it's coffers. The colonists wanted representation in Parliament and tried to mend their relationship with Britain but instead Britain considered the colonies to be in rebellion.

For money

Yeah, Why? Is there a book or three hundred about it in your local library?

Because the business interests in England didn't want settlers moving over the mountains and scr&wing up the fur trade w/the native tribes.

££££££££££££. Also, most of the Americans who fought for independence weren't "seeking a new life"; they were mostly descended from families that had been there for a few generations already.