Why do news people (weather broadcasters) refer to the area of the US around the Great Lakes as "The Mid-West"? Anyone can look at a map and see it is neither 'mid' nor 'west!'
Truth is ... I (think that I) rarely use the term because I (like you) think the region frequently called "Midwest" is neither "mid" nor "west."
However, it is possible that I have referred to the region as "Midwest" because that is indeed what it is called. As proof, look at the attached link:
The "Midwest" is huge, extending from the Upper Plains and upper Mississippi River Valley eastward to include much of the Great Lakes region (exclude NY and PA) -- and even includes Ohio!
How can that be?
One definition: "Mid" includes any state east of those states that reach into the Rockies and those states west of the original colonies. Remember, Kentucky and Ohio were the "western frontier" less that 300 years ago! So, part of the term is simply a "holdover" from the past.
But also look how wide the "Midwest" is ... roughly as wide as the "West." So why is the "east" so narrow might be the better question. (Answer: greatest population for much of our nation's history in a narrow belt of near-coastal development.)
These "geographic" terms are worthy of debate, and should not be taken to mean exacting standards. Would you consider Delaware to be a "southern" state? West Virginia is also included as "South," yet the reason that the state exists is at least partly because residents there did NOT want to be "southern."
And there are a boatload of Lubbock, Amarillo, Odessa and El Paso residents (west TX) that would call themselves "western" long before they would agree to "southern."
Bottom line: in some cases, the terms are not geographically correct but simply convenient.