If you use a sextant and measure the size of the sun it comes out a 32 arc minutes as you can see in the table linked.
https://en.wikipedia.org/wiki/Angular_diameter#Use_in_astronomy
1 degree = 60 minutes of arc.
1 minute of arc = 1 nautical mile.
It's that simple.
Unless I'm misreading you, you seem to be saying that one arcminute of apparent diameter is necessarily equal to one nautical mile. That doesn't make any sense.
A nautical mile is a minute of arc of a great circle on the Earth's surface. That's a different sort of thing from measuring the apparent angular diameter of an object from the Earth's surface. Maybe I'm dense, but I don't see how the two are related.
http://www.suomennavigaatioliitto.com/files/manual/mark15_25.pdf
A NAUTICAL MILE is equal to one minute of arc of a great circle. Latitude is measured north or south from the equator along a meridian (a great circle). One minute of latitude equals one nautical mile anywhere on the earth. Longitude is measured east or west from the prime meridian (zero degrees) at Greenwich, England. It is measured along a parallel of latitude (a small circle). One minute of longitude equals one nautical mile only at the equator. Approaching the poles, one minute of longitude equals less and less of a nautical mile.
Stop blindly parroting things that you see in Youtube videos for a moment and think about it: if you went outside and measured the apparent angular size (height, in this case) of a building in the distance with a sextant at, say, one degree of arc, would you conclude that the building is 60 nautical miles tall?
Don't come back to this thread unless you have a source as specific as this disproving my source.
Jesus Christ.
Your source literally just writes "1 minute of arc = 1 nautical mile" on some scrolling text with some animations about electricity or whatever. Hey check it out I've got some really "specific" sources here disproving your source:
Dr David Thork is terrible. He is.
It even moves and everything.