Why don't we just call the place dc so as not to confuse with Washington the state?

The term "DC" stands for Washington, D.C. (District of Columbia), which is a federal district and the capital of the United States. While it could be convenient to refer to it simply as "DC," the full name helps distinguish it from Washington state, which is a separate entity located on the West Coast. Additionally, "Washington" alone often refers to the state, so using the full name or "D.C." provides clarity in communication.