Who needs facts when I got my gut?

When I get in to arguments with people about data, most of the conversation is pretty predictable.  Sometimes people counter with contradictory data, claim my data is biased, is from a bad source, is outdated, irrelevant, or otherwise not worthy of consideration.  I can accept this.

The one thing that really baffles me is when people just say "No, that's not true", and when pressed for why explain that their personal feelings lead them to believe that what I said can't be true. 

I was thinking of this today during a talk at a conference I was attending.  The speaker was giving an interesting talk about the phenomena of having many STEM jobs open during a time when there was high unemployment, and why there was a "talent gap".  She finished her talk, and a woman raised her hand and said "You say there are jobs, but there aren't.  I know because I'm unemployed, and so are two of my friends."  

The speaker (who works for a recruiter, btw) sort stammered with a bit of confusion, and repeated the numbers she had shown originally that showed there were jobs out there in these fields (at least in this city), and the length of time many of them had been unfilled.  The woman repeated "Yes, I see that, but I don't have a job, so it's not true."  The speaker did pretty well from there, putting a few more things out there until it became entirely clear the woman believed that all economic activity rested on whether she personally had a job or not.

Now of course we all have cognitive biases.  That's why we have science and data...because humanity has realized our eyes deceive us at times.  What baffles me is when people are willing to pipe up in public and say directly "no, I will only believe what I see".  

Perhaps I should appreciate that it's not subtle and insidious ignorance, but it still gets me every time.