Why are the "hands" of a clock called "hands"?

They do resemble pointing hands; especially the classic style of hour hand. Yes, they're thinner than human hands, but they point:

Etymonline says this usage of hand is over 400 years old:

Clock and watch sense is from 1570s.

Other than that, I don't think anyone can explain just why clockmakers chose hand instead of arm, or even finger. The point is that they point, like a hand.

Human hands can be used as a sundial, dividing daytime into 12 equal "hours." You have to go outside to do this: Strerch one arm straight out in front of you. Hold your fingers straight and fold your wrist in at a 90 degree angle. Now raise or lower your hand until your pinky appears to just touch the horizon. Now take the other hand and "stack" it on the first. Then move the first hand and stack it on the second. Continue alternating hands in this manner, and you will find that it takes about six hands to go from horizon to directly overhead. So... six hands up and then six hours down divides the daytime onto 12 equal parts.

The concept of dividing daytime into 12 hours predates clocks. As does the concept of noon as well as, of course, the human hand. My guess is the pointers on the clock got their name from their being a timekeeping replacement for the human hand.