Why isn't it taught that George Washington was not the first President of the United States, but the first one under the Constitution?

Because George Washington was the First President of the United States.

Prior to the creation of the Constitution, the position was not “The President of the United States.” The position was the “President of the United States in Congress Assembled” or, more commonly, “The President of Congress.”

Given the nature of the Articles of Confederation, the President was not the position we think of now. There was little power in the office, it had a term of only one year, and in many ways was ceremonial, similar to the Constitutional position of President of the Senate held by the Vice President of the United States.

The men who held the position are not considered “President of the United States” for those reasons as well as for the fact that the Articles of Confederation was a failed system that did not create an effective system of governance. These same men realized a new system needed to be created and they did so.