The wave nature of light does not explain everything we see experimentally when working with light (notably, the photoelectric effect), therefore, the wave model of light is an insufficient model.
Likewise, the particle nature of matter (particles with mass, like electrons and protons) does not explain everything we see experimentally when working with matter. Here, you've got experimental results like the diffraction of C
60 that mess up the traditional particle model of matter (
Nature: DOI
10.1038/44348).
Until someone comes up with a better model, wave/particle duality is the best explanation we can come up with. Just because you don't like it doesn't make it a poor model to fit current experimental evidence.