I always wear my TIG gloves when operating grinders and was glad I do a while back when my hand made contact with the wheel: what would have been a nasty and painful gash ended up being a scuff mark on my glove.
But that raises another question: Why on earth would your hand be anywhere near the head of an operating milling machine?
EDIT: Thinking about this more, we might have different concepts of "glove." TIG gloves are thin, tight-fitting, and leather.
They also have a "gauntlet type" cut that extends up your forearms and over your sleeves. I don't think they'd be any more likely to catch a machine part than your skin would, and I think they'd actually reduce the chance that a sleeve gets caught.
OTOH, it makes sense that the thick, heavy fabric gloves that are used for MIG or stick would make your hands more clumsy and prone to getting caught in machines. I agree that those are probably pretty dangerous.
Accidents happen. You slip, or get tired and careless and then suddenly your hand isn't where you expect it to be. On a manual mill, it's more likely that your face, not hand will be closer to the bit as you monitor how it's cutting.
A chemistry senior was killed by a lathe at Yale last week working alone late at night when she was pulled against the machine by her hair.
An average size lathe with a 6" chuck will pull 18" of hair in a single revolution. At a moderate speed of 300 rpm that's too fast for a person to react. In the battle of human vs. 3hp motor, human loses. I've seen enough photos of human bodies turned into hamburger by even small industrial machines to not take the danger seriously!
That shop, at the local community college, is the only one I've ever used, so I can't guess what practice is more common.
also when you zero out a mill, you need to touch off a tool (don't know the name) to define your origin spot. it's not sharp and you should spin it at low RPM, but it's still moving, and you shouldn't have gloves anywhere near it.
That is probably the only reason training is so important.
But yes you'd end up hurt either way.