Water isn't wet because it is a liquid that wets things. Once you come into contact with water you become wet. Until then water is liquid and you are dry.
Water is a very weird substance. It is sticky yet we do not think of it as sticky. Think about it. Water sticks to clothes, hair, skin, almost everything... Water, itself, is not wet. It is a substance that sticks to other things and the result of this stickiness is what we call “wet”.
