"DC shouldn't become a State because it isn't a State" is the most ridiculous circular reasoning.
Every State wasn't a State, until it became a State. One of our States was a Republic; another was a @#$%ing Kingdom. The whole nation is built on taking areas that aren't States, and turning them into States.
DC was established as a concept in the Constitution in 1789. It was carved out of Maryland and Virginia in 1801, then the Virginia land was returned in 1846. It wasn't made a single district until 1871, and then its representation was overhauled with the 23rd Amendment in 1961. Its makeup has not been static for these past 230 years; it has been changing constantly and, as stated, it has a higher population than three States. There is no reason it can't be one itself.
Until then, there are almost 700,000 American citizens with no voting power in the House, and no representation at all in the Senate. That goes against our entire belief system.