Here's the basic issue, in my opinion:
As used in the WSFS Constitution, "fan" is not the opposite of "pro."
Fan and Pro are not radio buttons; they are check boxes. You can be one, both, or neither. "Fan" <> "Amateur."
This troubles many people for whom "fan" and "pro" are polar opposites, and once one becomes a pro, one is never again a fan. I don't agree with this.
It also troubles some people that while the WSFS Constitution uses the descriptive term "professional," it doesn't try to define it in a technical sense. Just as no two people are likely to be able to agree on a definition of "what is science fiction," it turns out to be very difficult to have a clear and objective definition of "professional" that applies in all cases. Therefore, just like we let the voters decide what is SF/F, we let the voters decide what is "professional" and what is "fannish."
I've been accused of advocating a "tyranny of the majority" with a negative implication. This annoys me. Frankly, the Hugo Awards voting is a tyranny of the majority, and majorities have rights, too. Disagreeing with the taste or judgment of the voters is not the same thing as saying the rules themselves are wrong. Since the Hugo Awards are popularly voted by the members of the World Science Fiction Society, they will have all of the perceived faults of a popular-vote award. You can avoid those by having a small select jury select the winners, and then you trade the popular-vote faults for the small-committee faults. You can't please everyone.
What many people don't seem to realize is that advocating for Hugo Administrators to be more activist and to "make the right decision" (in this case, some say that Pohl this year and Scalzi
It is precisely because we give the Hugo Award Administrators strong authority over certain aspects of the Awards that we also strongly discourage them from actually exercising many of those rights. Indeed, it occurs to me that most non-techincal actions by Administrators (such as disqualifying A Brief History of Time back in 1989 because it wasn't sufficiently SF/F/Fandom) are analagous to the British Monarchy's residual powers such as the power to withhold Royal Assent: you can do them once and once only, because you'll never be allowed to do it again.
Update: Fixed reference above from comment.