[Boogieman]

Well, because waves are simpler and easier to match to the observed phenomena. Scientists already know that particles exhibit "wave-particle duality", meaning, they act like both waves and particles. WSM theory simplifies that by saying the "particle" is actually just a 3 dimensional standing wave pattern. Not only does that explain why particles seem to act like waves in many circumstances, but it also matches observations:

Tip of a platinum needle enlarged 750,000 times.

Field ion microscope image of a 'single crystal' tungsten tip.

Water standing waves formed with vertical oscillation in a circular dish

Interestingly enough, you can actually generate all the Platonic Solids and Kepler-Poinsot polyhedra simply by generating various 3 dimensional standing wave patterns in liquids. The number of vortexes of these shapes also just happen to coincide with the number of electrons that can fit in the various electron shells of particles, a key property of the elements of our periodic table.

[El Gato]

Your wave theory sounds very much like String Theory.