In the last Olympic games, I noticed that, in Taekwondo, fighters adopt a stance where both are facing the same direction. Is that forced by rules? Why not have a mirror image stance, so no one has an advantage?
Do you mean that one person has their left foot forward and the other their right foot, with their bodies "bladed" so that their chests are pretty much facing one direction? If so, there is no institutional TKD reason; one guy might be a lefty with their "power hand" in back. Or one or the other has reversed their normal stance as part of their sparring strategy, e.g., they think that their opponent might not be as used to moves and attacks from a "southpaw" stance.
This is the Taekwondo "back" or "side" stance, depending on what any particular Taekwondo school might call it in English. It's where your front leg has toes pointing forward, and your back leg has toes pointing to the side on a 90 degree angle. If you were to bring the feet together, they would form an "L" shape, or a right angle. That naturally means your body will face to the same side as your back leg's toes point, or slightly diagonal is more common.
This stance minimizes targets on your body, making it harder for your opponent to score a point.
Because of facing to the side, you will have one arm forward and one arm back. If the left foot is forward, then your left hand will be forward. And vice versa. This is the standard "fighting position" in Taekwondo.
Taekwondo is unique in the fact that it trains both sides of the body to a high degree. In practice, it's still not equal, but schools do make an effort to drill both sides. In other martial arts, being able to do your techniques on the other side of the body is rarely emphasized.
As a result, you'll commonly notice Taekwondo people like to switch from left to right facing stances all the time. They may have a preference and may stay facing one side throughout the match, or they might switch back and forth.
No, it's not required that both competitors face the same side. They can switch at any time.
Hope that helps.