People can readily enough create mathematical formulas that describe “how.” God is the only entity who could ever explain “why.”
That said, even when we think we can explain ‘how’, mathematically or otherwise, we usually are only giving partial explanations.
Yes, we know that charges need to balance, but why is that? What exactly is a charge? You can say, ‘well it's what occurs when there is a differential accumulation of ‘positive’ and ‘negative’ particles, but how does any particle, electrons, protons, or whatever, have a ‘charge’? There is no mathematical formula, to my knowledge, that can explain this. Millikan could do his oil drop experiment (his grandson lived with a previous mentor of mine), and gives us some information about electrons, but we still have no idea what makes them attracted to protons, but repelled by other electrons. Saying that the ‘positive and negative charges have to balance out’, is just using our own designations for the properties that these particles have, without really knowing how those properties are defined mechanistically.
In short, we know very, very little. We compare ourselves to humans who didn't know what ‘electricity’ was, and who thought the world was flat, but in comparison to what there is to be known, we are just like neanderthals watching an eclipse.