As the esteemed Borek has already mentioned, no matter how many layers of the onion you peel back, you're always eventually going to have to accept something as an axiomatic truth: it just is what it is. Where you draw that line will depend on a number of factors, including your education level, your specific interests, and the fundamental limits of knowledge.
At a molecular level, all important forces are electrostatic in nature. However, the application of these forces at the quantum level often gives rise to effects that aren't observed in classical physics. For example, a large part of bonding is due to so-called electron exchange, which has no classical analog - it's kind of like the ability of electrons to be in more than one place at the same time. Ultimately, though, the same basic rules apply: electrons create electric fields and magnetic fields that can interact with each other in either favorable or unfavorable ways. When atomic shells are filled, there is an electric field symmetry in place that, to a first order approximation, removes all "handles" for interaction. An unfilled shell has an asymmetry that allows the atom to interact with other nearby charged particles (provides a handle for sticking together). Think of bringing two magnets together. Once two magnets are sticking, the asymmetry is resolved and more magnets will not stick.
Of course this is just first order approximation. There are things like induced dipoles and such that we lump together as van der waals forces, but again: how far do you want to go?
Push too far and you start asking questions like: what is charge and why do they repel/attract? These are questions for theoretical physicists and maybe philosophers.