I can see what you're getting at here, and perhaps "language of logic" is not the most accurate way to describe what software is. Maybe "language of complexity" or "language of systems" or something else. Someone could come up with better terms or metaphors here.

The difficulties you describe, however, assuming they aren't being caused by flaws or bugs, are part of the "language" we're talking about. I think one of your assumptions here is that logic is simple. That's true to begin with, but the software systems we build are usually towering arcologies of logic, with all manner of intricate, sometimes counter-intuitive details. A single detail, when examined by itself, is relatively easy to understand, but when taken together, they form a serious challenge for any human mind to grapple with. I think you could make comparisons to sprawling works of literature or advanced forms of mathematics, where the bits and pieces can be grasped, but the number of pieces, and the connections between them are often too difficult to see all at once.