Frankly... I don't understand how a photon interferes with itself... the fact of the matter is that all particles interfere with themselves. Electrons experience self-interference, for sure. I can't imagine this property is absent in quarks, but I don't know that it's been tested.

I guess my advice is to accept that you observe this property. If you are not convinced about it, look up or perform the experiments which demonstrate this property. Become convinced, or have a compelling argument for why you are not convinced. Whether or not it is intuitive is merely a statement about your history of exposure to the idea, I'd wager.