> Personally speaking, I've never cared whether someone "validates" my emotions (and I often view such attempts as a bit patronizing or insincere).

The solution is to be sincere. As to the reasoning behind it, it's not merely to appease the other person, it's to actually consider their point of view, because they might be right. If you don't consider their point of view then you're not considering all options, and more importantly you're willfully ignoring an option being presented by the person you are communicating with. That's not just dumb, it's disrespectful.