Vector2 is a value type. Therefore, when using Vector2 as a property, the setter will only return a copy of the Vector2 you want to modify. Every change made to it will directly be discarded, hence the compiler will not allow you to modify properties of a value type through a Property. You will have to set the Vector2 this way:
paddle.Position = new Vector2(x, y);
There are a lot of threads on the forums which explain the difference between reference types and value types. Just search for it.