Where is this idea that sociology can't be quantitative coming from?
Have any of the ignorami making this claim even looked at a sociology paper published in the last thirty years?
Any social science can and must be statistical or have some way to show evidence for its claim. Things you can't prove is called faith.
Austrian economics just makes a distinction between economic theory and economic history. Rational thought experimentation is the only thing needed to formulate sound economic theory. You can then compare that theory against the statistical record, and if they don't match either the statistics are the outcome of other factors or your reasoning was flawed somehow. But, if your reasoning is correct, it's impossible for your theory to be wrong.
This is utter, unmitigated nonsense. You cannot conclude anything based on nothing. Every reasoning starts with some assumptions: a theorist's stand on how the world is. Reasoning develops these assumptions into (hopefully, observable) implications. There is no reasoning that can tell you that humans choose by optimizing a preference relation (the starting point of much of modern economics). It is a theory that, one hopes, will explain observed data. Logical reasoning is needed to understand what are the testable implications of preference maximization.
Similarly, say, the law of gravity in physics is not derived from logical reasoning: like every "Law of Nature" it is, essentially, an empirical statement. This particular empirical statement has been consistently confirmed by observation for so long that, if on observes a violation (say, an apple flying off into the sky), one will indeed be pretty certain that something is wrong with observation. However, if somebody designs an experiment that shows that under certain conditions apples at least sometimes fly off into the sky in a manner inconsistent with gravity laws as currently known, these "laws" would have to be reformulated: not because of any logical flaw, but because they would turn out to be at odds with reality.