The loudest economists use economic theory as a cudgel. You are right to find them infuriating. They assert certainty where economics does not, and cherry pick exceptions to hold up as rules. They are to economics as RFK Jr is to medicine.

The math of economics is more like the math of epidemiology or fluid dynamics than the math of mechanical linkages. It describes how things tend to interact within a system, but a given element or interaction is unpredictable. Even concrete sections, like price theory, have contradictions like the velvet rope effect. It describes probable outcomes in a chaotic system running on irrational humans.

Meteorology is still a math-based science that makes useful predictions, even though it cannot say with certainty whether a particular tropical depression will become a hurricane.