Arithmetic is taught in grammar school, and the algebraic notions required are really just first-year high school algebra. Surely none of us have problems understanding the basic tools. The difficulty, I think, lies in the generality of approach that is necessary for proper use of arithmetic methods. Consider the example I used earlier. But the more general arithmetic form defies clear verbal expression.
Arithmetic expressions are more abstruse than boolean expressions.
It is the abstruseness of the arithmetic expression that repels the incompetent and attracts the perfectionist. Yes, arithmetic methods are more difficult to use. They are more difficult because they are more powerful. Yes, we have to think harder to use them.