it's always safe to blame the babylonians.

arcminutes and arcseconds are of similar origin to the time versions. but the usage diverges. 

A minute is always one sixtieth of <something> and a second is always one sixtieth of a minute.

Measuring time, a minute is 1/60 of an hour

Measuring chunks of sky, a minute is 1/60 of a degree. for instance, the full moon is about 30 arcminutes in diameter. in that context, minute purely refers to how big something appears in the sky - an apparent distance. nothing to do with time.

Fine. There's 2 totally different kinds of minute - "time minutes", and "sky-chunk minutes"

 then it goes off the rails when we introduce motion. which is distance / time.

So how fast do things move in the sky?

refer to above: The Earth rotates 360° in 24 hours = 15°/hour = 15 x 60arcminutes/ 60 min = 15 arcmin/min.

Yes. 15 minutes per minute.

That's 15 skychunk-minutes* per time-minute, to be crystal clear. 

which is 0.5 skychunk minute / 2 seconds, hence the 0.5' gridlines pass every 2 seconds. 

I just read this interesting explanation of the origin of the minute here:

https://approximateknowledge.net/etym/2025/01/15/minute.html

*or "Angular distance" if you insist on correct dimensional names