Trying to apply rationality in domains where it's ineffective is obviously a bad thing. In the real world, only a limited subset of issues can be reduced to logic and calculations. To believe otherwise is pure hubris, and if you've read the classical tragedies you know the results.
See Hamlet, who famously lost everything after basing his charitable giving strategy on pure reason.
What now? The main thing about rational (logical) arguments is to make explicit the domain of their applicability and ensure that fits the given situation.
The social myth of important social questions not being amenable to rational consideration is a political tool, not scientific truth. The classical literature doesn't help there.
I suggest you read the 2 cultures, that will help you navigate this issue.
Most people do not believe that everything is measurable unfortunately
https://en.wikipedia.org/wiki/The_Two_Cultures