Because the Declaration of Independence was signed on the 4th of July, and without that declaration, the revolutionary war (and the Treaty of Paris) never would have happened.

I have often wondered about this very question. welcomehome , if you don't mind, can I expand your question to be about why most New World countries celebrate their independence day on a date when a declaration of independence was made, or when military action commenced, rather than on the day when they actually became independent?