How do you argue with someone who’s confused a lack of emotional connection to a topic with objectivity and rationality? Say a topic profoundly affects you and those you care about, but not the other person, so you get angry and flustered and they seem to think this means you’re less objective as a result and it’s an easy win.
One solution is to question their competence to speak on this subject, and assert the superiority of lived experience over purely theoretical knowledge.
Another solution is to weigh (their) rationality against ethics. Many purely rational policies have led to disasters and horrors. Eugenics, for example, is perfectly rational.