The primitives of control flow in programming languages are sequencing, if, while, for, switch, return, and "early return" (goto restricted to exit a containing block). We might compile these into a form that represents everything using conditional jumps, unconditional jumps, and jump tables, but that's not how people think about it, definitely not at the level of programming languages (and even in the compiler IR phase, we're often mentally retranslating the conditional jump/unconditional jump model back into the high-level control flows).

And I could go on with other topics. High-level languages, even something like C, are just a completely different model of looking at the world from machine language, and truly understanding how machines work is actually quite an alien model. There's a reason that people try to pretend that C is portable assembler rather than actually trying to work with a true portable assembler language.

The relationship you're looking for is not arithmetic to calculus, but set theory to arithmetic. Yes, you can build the axioms of arithmetic on top of set theory as a purer basis. But people don't think about arithmetic in terms of set theory, and we certainly don't try to teach set theory before arithmetic.