Why do not waves exist? There are, only the word wave is an adjective, which describes the object. Object can be anything you like.
And it is quite true that this is the theory. And the THEORY is proven, but who has proved the existence of waves? The theory and assumption for me are different things.

Physics is more than words. Physics aims to describe reality, make predictions about the results of any experiment (in the broad sense) that should be carried out. Whilst waves were originally connected to fluid dynamics, the concept is more general and applies to varied fields.

For instance, one hears sound. Sound is a vibration that propagates and that our brain materalizes somehow. It is thus a wave. In the physics sense of it. I am sure you would not argue that sound does not exist.

PS: I am fine with the arguing/no arguing part. We are jus chatting and there is nothing wrong with that :)