You are assuming that there is graspable meaning or reason to things beyond their mathematical expression. At the limit, this may not be the case. A theory may well be "this is the mathematical expression the most adequate for the purpose of making predictions about this particular phenomenon". It may not cover the why, although theories tend to have common qualities, and have a tendency to have nice symetries and talk about preserved quantities.

Imagine that at the end of the day, we will find that some quantity which we will be able to measure, shlurm, is conserved, and that through clever math, we can use that to deduce the rest of physics. Call this shlurm theory. This is the ultimate theory of everything, there is no ambiguity, no magical constants other than the total amount of shlurm in the universe. We will never know why shlurm is conserved. We will have to accept that the universe is wholly described by this mathematical construct and no other. QCD is a bit like that, except for the final, definitive bit, and the single constant bit. And the whole of physics bit. But the point is that interpretation does not matter, not having an interpretation of QCD does not hinder its study or usefuleness, or its explanability.

Also, it's quantum field theory, and yes, the tool is quantum mechanics. But there is an underlying theory. It talks about the mathematical shape of reality. It cares not about why this shape is.

At the end of the day "why" is for theology, because you will have to accept that _something_ is some fundamental truth on which everything else is constructed.