The water in the bottle, like everything on Earth, is being pulled down by Earth's gravity. The bones in your body or the rigid legs of a table allow you and the table to stand up under this pull, but liquid water has no structure.
Like the surface of a lake or water in a bath tub, the water in the bottle will be pulled down so it has a flat surface. As you tilt the bottle, the surface stays parallel to the ground because gravity is still pulling it straight down. When the bottle is tilted so far that the surface goes through the mouth of the bottle, the tiny water molecules by the mouth no longer have anything to support them. With no wall next to them to hold them up, the water molecules tumble out through the mouth of the bottle. When the ones closest to the mouth fall through, then the molecules next to them no longer have anything holding them in place and they will flow out the mouth as well.
If you stop tilting the bottle at this point, you'll see the flat surface of the water now lies right at the level of the mouth of the bottle. If you turn the bottle over quickly, the water will still take time to pour out because it can't all fit through the mouth of the bottle. Just like people leaving a plane or a movie theater, the water molecules have to wait their turn to file out through the mouth.
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