This concept is far easier to illustrate than to explain. So here are some examples that prove water is NOT wet.
Heat! Wetness is like heat. When you touch a hot object, you feel heat, but the object itself isn't "heat." Similarly, when you touch water, you experience wetness, but water itself is not "wet."
Fire! Fire can burn things, but fire itself is not "burnt." Likewise, water can make things wet, but water itself is not wet.
Color! A blue ball has the quality of "blueness," but we wouldn't say the color blue is a ball. The ball is just an object that has the quality of the color blue.
Electricity! A battery can provide electricity to power electronic devices, but the battery itself is not "electricity." The battery stores electrical energy and can transfer it to other objects, allowing them to function. Similarly, water has the quality of wetness and can transfer that wetness to other objects when it comes into contact with them. However, this doesn't mean water itself is wet, just like the battery is not electricity.
Light! A flashlight can create light, but the flashlight itself is not "light." Just like that, water can make things wet, but the water itself is not wet.
So is a flashlight light? Of course not. And for that same reason, water is NOT wet!