The issue people are having is, that you start out with "sort of" as your response to the statement that math is the study of precisely-defined terms. In doing so, you decide to throw away that insightful and useful perspective by confusing math with attempts to use math to describe phenomena.

The pitfalls of "mathematical modelling" are interesting and worth discussing, but it actually doesn't help clarify the issue by jumbling it all together yourself, then trying to unjumble what was clear before you started.