I think you've taken the advice of your shop teacher way too far. Sure. Loose clothing, including gloves, are an absolute no-no around power tools such as drills, saws, mills, lathes, and such.
But I always wear gloves when working on the car, doing yard work, hauling supplies. There is no way that I would do winter activities without a good pair of gloves. And a nice pair of grilling gloves make handling cooked meat so much easier. And a pair of welding gloves are almost a must when dumping hot charcoal out of a chimney lighter, and spreading them in a grill. I always wear a pair of elbow length rubber coated gloves when working with drain cleaner, and wouldn't think of working with household chlorine without a pair of gloves.
In my teen years I worked on farms during the summer. I learned very early of the value of a nice pair of leather gloves. Not only do they keep your hands clean, but they protect your hands and give a better grip. The right pair of gloves for the job make all the difference in the world.
So, yea, I really like wearing gloves when the job calls for it. Are they annoying as the dickens when you need to do fine work? Sure. but the neat thing about gloves is they come off, unlike severe hand damage from, oh, lets say frost bite, chemical burns, heat burns.