It's because that's when the big battle at Fort Sumpter took place and Francis Scott Key wrote the Star-Spangled Banner was written
And we officially declared ourselves free from British control.
It's the day that the Declaration of Independence was signed by those men in Boston. The ones who realized that the government should be BY the people and FOR the people. NOT for the government only. Not for the politicians to make a career out of being in DC. Not to further their coffers but to make the USA safe for the citizens.