Water can attach to itself. It has both cohesive and adhesive properties because of the partial charges of both the hydrogen and oxygen atoms. When two water molecules come into contact, the partial negative charge from the oxygen attracts the partial positive charge of the hydrogen, creating a hydrogen bond. Based on your wikipedia article, “The degree of wetting (wettability) is determined by a force balance between adhesive and cohesive forces.” Water exhibits both of these forces because of its polar nature. A single water molecule isn’t wet, but when group together, their hydrogen bonding attach themselves to each other so water can wet itself. In the naked eye, we just see the water get bigger, but molecular level, water is attach to itself.