When the sun hits your watch, you’ll have a beam of light on your wrist. Unless you want it in your eyes, you should wear your watch upside down. Military personnel are usually out in the sun, so this is especially true for them.
They aren’t the only people who go out in the sun. Sportsman do as well, which is why you’ll see them wearing their watches upside down.
Let’s not forget that hospitals get pretty bright too. You’ll likely see nurses doing this too.
Not only do special forces personnel need their watches to be easier to read, light discipline is also very important.
Light discipline is how well you conceal yourself from the enemy. When rays from the sun or moon hit your watch, not only are you making it harder to read, you’re showing your enemies where you are from miles away.