You don't decide to sleep with your mouth open. Nobody does. It happens quietly, sometime after falling asleep, and you find out the next morning: through a dry throat, a comment from your partner, or a photo that never should have been taken. There is a real, physical explanation for this, and it has almost nothing to do with willpower.
Your jaw is kept closed by muscles, and those turn off
As long as you are awake, the muscles around your jaw and mouth remain slightly active without you ever thinking about it, keeping your lips gently closed on their own. As soon as you drift into deeper sleep phases, this muscle tension drops significantly, just like everywhere else in your body. Without this constant, quiet effort, gravity takes over. And for many, that means: the jaw simply drops down and open by itself.
Sleeping position makes it worse for some
When you are on your back, gravity acts on your jaw differently than when you are on your side. Lying flat on your back, there is nothing for it to rest against, and the jaw can only drop down and open. Side sleepers often notice this less, simply because their jaw is resting on something instead of hanging into thin air.
The connection almost no one makes
This is the part you should really understand. An open mouth and mouth breathing are related, but they are not the same thing, and very often one triggers the other in a specific direction. If your nose feels even slightly congested, your body prefers mouth breathing to get enough air. And an open mouth is what that looks like from the outside. So, relaxed muscles explain why the jaw can physically open. A congested nose is very often the actual reason why your body allows it.
Why this becomes a cycle
As soon as your mouth is open and you are breathing through it, your nasal passages are used less for part of the night. A path that is used little can become slightly less efficient over time, and the next time, the nose feels even more like the harder option. A small, self-reinforcing loop. This explains why some people feel their mouth breathing has gotten worse over months instead of staying the same.
What really breaks the cycle
You cannot force your jaw muscles to stay active while you sleep. This relaxation is part of deep sleep, and that is not something you want to interfere with. What you can influence is which option feels easier for your body. If your nasal passage is open and functioning well, a large part of the reason why your body reaches for the shortcut of mouth breathing disappears. That is a much more sensible starting point than trying to consciously control something that happens when you are long asleep.