Suction cups work by the shape of the cup forcing a vacuum underneath it, which causes air pressure to force the cup closer to the vacuum.
Unfortunately, if any air gets under the cup the vacuum is broken and the cup falls off.
Fortunately, glass is flat enough and suction cups are flexible enough that where they meet there is almost no room for air to pass through, so the vacuum can stay stable for quite a while.
Unfortunately, neither the glass of the mirror nor the material of the suction cup is perfect. The little bit of room for air to pass through will break the vacuum in a matter of hours most of the time.
Fortunately, water can be used to fill those imperfections instead of air. As long as the water is there (which can be months, since there’s no air to evaporate it) the vacuum will be protected.
Suction cups work because there is suction underneath the cup. This suction is a result of lack of air under the cup and all the air outside the cup pushing down on it. When you put water under a suction cup you get rid of the air, but you don’t get suction because you still have water under the cup. But since water is a noncompressable fluid (Meaning you can’t put it under pressure and reduce the volume you can only kinda push it around) and air is compressable (meaning you can place it under pressure and change its volume), if you fill all the space with water instead of air and then press on it, it will push the water away and then have no air or water making a strong suction. This it is a lot easier than trying to press the air out on its own.
So ultimately water is easier to push away than air, and so it is a lot easier to get rid of the air with water and then get rid of the water, than it is to just try and get rid of the air outright.
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