Why Can't People Disagree Without Taking Things So Personally?

I think a not-so-obvious reason is the relativism of modern moral discourse, best expressed in the theory known as “emotivism.”
In After Virtue, Alasdair MacIntyre wrote that “emotivism has become embodied in our culture.
He defined it as “… the doctrine that all evaluative judgments and more specifically all moral judgments are nothing but expressions of preference, expressions of attitude or feeling.” In other words, emotivism holds that there can be no way of rationally justifying one’s claims about those controversial issues mentioned above. (Intellectual Tackeout).

The basis of our actions aren't rational. Rationalizing is mostly the process whereby we narrativize what we've already done or were going to do anyway. So the issue isn't just about emotional relativism -- it's deeper than that.

It's that we literally don't know why we do what we do, but we have involved stories about why we do what we do, which we call "my beliefs" or even, "me." Might some be rational and some not?  I'm still somewhat unsure about this, based on the various interpretations I've read of post hoc consciousness etc. Maybe research has pointed in directions I haven't caught yet but it seems equally possible that our more cogent rationalization is still a blind, it just might also lead to more valued or preferred results. So we call this "truth" -- and yes I know this is a very William James kind of thing to say.

All It Takes Is The Right Story. Mythos Media