Ironically, the author of this article lets emotion distort his thinking on the subject of the way emotion distorts thinking. He's looking at an experiment where people were asked "to interpret a table of numbers." When the numbers related to an issue they had opinions about (gun control), they made more mistakes than when the subject was neutral. They tended to err in the direction of supporting the beliefs they already had.
But emotion is part of reasoning, and it's impossible to function in the real-world lives we live without jumping steps intuitively. When you think you already know the answer, you don't study the details so much. That makes it harder to get to people with new information or to readjust biases, but it's not depressing. It's the normal functioning of the mind, and it's exactly what one would expect. We don't rebuild our understanding from ground level every time we think about a familiar topic. We'd never get as far as we do putting ideas together if we had to stop and scrutinize and recheck every element of what we believe and what we think we know.
Of course, it's important also to be able to slow down and get critical, but we have individual autonomy about when to do that, and a study that tells people to do a particular math problem does not unleash the individual will. It's an imposition of authority from the outside, and it comes with no intrinsic reason to be precise. So people take the shortcuts they think they know, and they make mistakes.