While reading Rhetoric by Aristotle, it became clear to me why that tweet always bothered me:

When making your case to an emotional audience, Aristotle points out that the dialectic -- such as facts -- won't work. The reality is that their feelings simply don't care about your facts. Again, it is the responsibility of the speaker to account for this; the fault isn't with the audience.

I don't know what Ben Shapiro was thinking when he wrote that. Maybe he means that feeling like something is true doesn't make it true. I don't know. But I don't like the man, and so I won't spend too much time defending him here.

The point is that feelings don't care about facts.

When making your case against an emotional person, you can't persuade them with facts. This is because you aren't trying to change a mind -- you're trying to change a heart.

Emotional people are driven not by statistics, but stories. A story about one suffering person will upset them so much that they will be driven to support laws that affect an entire state. Even if you show them a pie chart that proves that every one else is doing just fine, they will still be scarred by the story of the individual who was struggling to survive.

"Know your audience" holds true, once again. If your audience is able to be persuaded by facts, then that's your best option. If your audience is not persuaded by facts, then emotion will be your guide. Flexibility is important. Stubbornness and "sticking to your principles" will not achieve victory.