Earlier quoted context omitted.
I'm an engineer too, and I fully agree with you. My particular peeve is engineers who kowtow to economics, putting it in a much higher pedestal than sociology or anthropology, because it is "mathy". The implicit assumptions are usually along the lines of "the assumptions seem obvious enough, and look at all those formulae in the transformations thereof!"
Science id defined by its method: to set up experiments in order to look for counterexamples for a theorem. It is pretty much impossible to set up experiments in economics. While I agree that sociology and anthropology do not satisfy the definition of science, economics does not either. Where are the experiments? Without experiments, no science.
This is the example used in methodological discussions of economics. I don't know if astronomers do actually perform experiments on some limited scale, but it seems that classicaly they relied on "luck" to test predictions e. g. testing general relativity through observations of eclipses. In social sciences, there is a somewhat similar thing called "natural experiment", which is the main test for the validity of predictions. In both cases, the researcher takes a more passive role in testing his predictions.
This can be dauting to researchers, but overall it's for the best. There are indeed experiments in economics, specially in game theory. But the majority of possible experiments would cross the boundary of what is morally acceptable, and well into morally abhorrent e. g. randomly restricting a sample's access to education to estimate it's effects on wages.