Most people have no clue what criticism is supposed to do. They see it as negative because it produces some sort of pain, but they don't realize that pain is evidence of their continued growth--which is what it would be if they accepted it for what it is. But because they reject criticism as anything valuable, they don't grow. They stay mired in the mediocrity that produced the criticism in the first place.

However, I've noticed that such people tend to be quite critical of others.

People often confuse criticism with critical thought. The two are very different. And until one knows the difference, one can offer constructive criticism.