There is nothing puzzling about an ordinary macroscopic classical wave travelling through two slits at once in this way. A wave, after all, is just a ‘disturbance’, either of some continuous medium (field), or of some substance composed of myriads of tiny point-like particles. A disturbance could pass partly through one slit and partly through the other. But here things are very different: each individual photon behaves like a wave entirely on its own! In some sense, each particle travels through both slits at once and it interferes with itself!
Interesting to note the difference between particle and wave like duality. Waves perturb existing matter, and particles are the substantive mass.
