There are a few reasons why special forces personnel wear their wristwatches upside down (or inside facing out).
Less Damage To The Watch
Soldiers do a lot of work outside and reversing the watch can prevent unnecessary damage to the watch face. Bumping into things happens often – doors, walls, counters, handles, etc.
While working indoors, it’s smarter to flip it back to normal as they might scratch it against keyboards, filing cabinets, boxes, or whatever else.
Many people choose to switch around their watch depending on the task at hand.
Keeping your watch on the inside of your wrist puts the time in your face multiple times per day. It’s somewhat unnatural to turn your wrist to check the time.
Consciously (or unconsciously) they become more aware of the time.
Plus, it’s much easier to check the time using minimal movements and without taking your hands off the rifle. Although, checking the time should be the last thing you’re doing if you’re engaging the enemy.
The shine from the sunlight reflecting off the watch may give away their position.
Mud, jacket sleeves, scrim nets, or watch covers could get the job done too, but it’s much easier just to turn the watch around.
However, real operators will be wearing $400 Tacticool Gloves which cover the wristwatch anyway. At the end of the day, soldiers wear a watch in whatever way they find the most comfortable.