The best answer I've seen regards professionalism. We require degrees from doctors and CPAs and passing the bar for lawyers not because it's a guarantee of quality, but because it indicates that the person has a certain minimal level of understanding of the field's Body of Knowledge. Having that knowledge means that they are less likely to totally screw up and they have a rational basis for finding a solution to whatever ails you. Requiring a degree in CS, SE, or EE (I don't see the point of requiring a degree if it's not directly related to the field) does exactly this.
Of course, the argument then becomes should we be regarded as professionals or "just" programmers & hackers...
Disclosure: I have a BS in EE and an MS in SE and once seriously considered becoming a registered Professional Engineer (PE). I'm also a card-carrying hacker and I disagree with the article.