Not to disagree with you, John ('cause I definitely do not in terms of the point you're making) but I think the point of the comic is not that intuition is bad, but that the PHB using intuition (which in his case IS based on a complete ignorance of data) is akin to witchcraft.
One could go so far as to say that if it feels right to the PHB, it is almost certainly wrong and vice versa. (There have been some very rare instances of him being right.)
I think from a psychological viewpoint, 'intuition' basically means going off a lot of data that you're only aware of subconsciously.
The advantage of that is that your subconscious can process many orders of magnitude more data than you can consciously.
The disadvantage is that your subconscious is also much more vulnerable to logical fallacies.
All in all, obeying your intuition isn't always a bad thing. It depends on the !$%*!$%*!$%*!$ For solving math problems, you want to think logically - for making weather predictions, it's usually better to use your intuition (because of the amount of data involved). It isn't the same as 'ignoring the data'. Of course I realise that this comic is just a joke, but I think it a public service to point out the facts behind the matter to whoever may be reading, because understanding this can really help you deal with some problems better and appreciate other people more (since their gift for intuitive thinking may be better than yours, and it's good to recognise that skill, even if they aren't as good at more logical thinking).
The biggest problem when it comes to relations between management and engineers is that neither group tends to be very teachable. And while it's not unfair to label engineers as narrow-minded, managers are certainly not known as being,open to new ideas - at least not ones that aren't their own.
If engineers and managers just accepted that they stood to learn something from each other, things would be much better. As it is, engineers are frustrated by what they view as ignorance and stupidity among their managers, while managers are frustrated by the seemingly needless complexity that engineers introduce to discussions.
Both managers and engineers, at their worst, have lost complete sight of their company's overall objective, which is, of course, to make money.
Managers lose sight of the company's goals in favor of political considerations, making sure they get credit for successes, and remain blameless when it comes to failures.
Engineers, on the other hand, forsake the company's objective in favor of learning new things, and finding new and innovative ways to do things.
In both cases, whether it's management or engineers, personal goals usurp those of their employers, and ultimately confuse and frustrate the other.
@zpike - I did not use dictionary.com but an English Oxford free dictionary, which clearly gives the Latin and earlier English usage - the presentation within the page did not copy well to this website !