Question

Why didn't george washington sign the declaration?

Answer 1

George Washington, John Jay, Alexander Hamilton, and James Madison are typically counted as "Founding Fathers", but none of them signed the Declaration of Independence.

General George Washington was Commander of the Continental Army, and was defending New York City in July 1776. As instructed by John Hancock, Washington read the Declaration of Independence to the army on July 9th. 

Answer 2

Presumably he was rather busy as Commander-in-Chief of the Continental Army, a position to which he was appointed in June, 1775. The fighting was underway well before the Declaration of Independence was signed in July (or August, or November, depending on who you ask) of 1776. The battles of Lexington and Concord in April, 1775 are usually considered to mark the beginning of the war.