The short answer is essentially party politics. The long answer will take a bit.

In the first term of the Washington administration, one of the key/most controversial policy initiatives was Treasury Secretary Alexander Hamilton’s fiscal plan. A key element to this plan was the assumption of the state government’s debts from the Revoultionary war; essentially, the federal government taking the tab on States governments debts. Both the State and Federal governments were severely in debt, and Hamilton meant to establish the nation on good credit as well as give buisness leaders/wealthy individuals an incentive to support the infant Federal government (as the only way a lender who had lent the State miltia’s money would see a return on that loan would be if the federal government succeeded).

Now, the idea of the Federal government doing this today is not odd at all, but the contemporary opinion on the balance of power between the States and the Federal government was not uniform. Some, in Hamilton’s camp, expected the federal government to be very activist and make heavy use of something called the Elastic clause, which allows for congress to pass laws that are “nessecary and proper”, even if the Constitution doesn’t specifOthers, partisans of Secretary of State Thomas Jefferson and congressmen James Madison, wanted anything that is not specifically enumerated as a power of the federal government to be deferred to the States, following the Tenth amendment, and for the State governments to do the majority of the governing. Two things that should be noted; first, that this conflict is a natural outgrowth of seemingly conflicting language within the constitution. Second, there is something of a loose political party infrastructure. These aren’t the well defined and formalized structures of today, but more a loose system of “I support Jefferson’ and “I support Hamilton’. These loose systems would evolve into proper political parties in Washington’s second term, but these divisions are present in this time period, even if they are more drawn in sand then stone.

So Hamilton presents his report on the public credit, which outlines his rational for the debt assumption. While well received by Hamilton’s supporters, it was controversial among Jeffersonsonians; Madison argued against it in Congress and Jefferson argued against it to Washington. Eventually, it was evident that Hamilton could not get Congressional approval for his plan without a compromise from the Jeffersonians.

Three paragraphs down, and we finally get to D.C.

Another issue of the ages was where the permanent capital of the country should be. At the time, it was temporarily set in New York, with the understanding a more permanent capital was coming after ten years of time at New York. Obviously, every state wanted the capital to be within their borders. Every major city wanted the capital to be at their city, and no geographic region wanted the capital to be too far away.

How the following compromise happened is sort of a grey spot in history. Jefferson writes that essentially, Hamilton approached him out of the blue one day, and then the two hashed out the entire compromise over dinner, with James Madison in attendance. This is the popular historical interpration, which is obviously compelling; two founding fathers shifting the course of history over wine helps deify them as titans of history. What is more likely is that there was a series of conversations between the two loose political systems that concluded with the famous dinner date.

Regardless, the following compromise happened: Jefferson and Madison would not contest Hamilton’s debt assumption, and Hamilton would support a location for the capital close to Virginia, the duo’s home state, which would be palatable to both Southerners and Jeffersonians. Said location was a series of swamps around the Potomac river.

This led to the passing of the Residence Act, which set the nations Captial, and the assumption act, which assumed the States debts. Jefferson, for his part, called the compromise his worst mistake, as it was a massive victory for his nemesis, Hamilton. However, the debt assumptions arguably led to the good credit which allowed for Jefferson’s biggest victory in the Louisiana Purchase.

I did this all on mobile, so I apologize for any typos or formatting issues. I also simplified some issues, specifically the details of the constitutional issues (the issues of Federalism are constitutional law issues I consider to be beyond my knowledge) and the specifics of the Residence legislation/the actual construction of the White House. I don’t consider myself to have a sufficient knowledge of those matters to give a satisfactory answer.

Sources Ron Chernow, Hamtilon. Joseph Ellis, Founding Brothers. Joseph Ellis, American Sphinx.