You got it. People, especially mathematical physicists and philosophers (Aristotle in particular), want math to be something other than what it is. Math is nothing more than a symbolic language for describing relationships. In physics, it can be used to describe how things behave. But it can never reveal the cause for why they behave as they do, which is what so many really want to know, and want math and deductive logic to provide. The reason for this is simple: math identities cannot be physical identities. a(b+c) = ab+ac only describes the final outcome, not the mechanism/algorithm/"physical reality" (one multiplier versus two) that caused the outcome. To say that a math identity even exists, is to say that there does not exist a unique mechanism for obtaining any given value - the two sides of the identity are not in fact "physically" identical - only their "values" are identical. It is ultimately no different than saying that five pennies do not make a nickel, physically, but do add up to one mathematically. Hence, entirely different, often wildly different, physical interpretations (underlying mechanisms) can be assigned to the same math equation, because math identities enable one to rearrange the equation into a different form, thereby implying a different physical mechanism for evaluating the equation. Which form did Mother Nature chose to use? The math cannot answer that question. Only an actual observation, of Mother Nature's chosen form, in operation, can answer the question.
Rob McEachern