Professors are particularly disliked not because they are particularly powerful within the educational status hierarchy as a whole, but because 1) they are the technicians of the machine; and 2) they value, and embody, the values of the education status hierarchy more purely than their more powerful peers.
I was actually thinking about this earlier today. I was trying to determine what about certain professors bothers me. I was pretty sure it's present, at least to some degree in all of them, but something bothers me about some professors far more than others. It took me about 30 minutes of contemplation, but I think I figured it out. I probably won't go over well with current and aspiring professors and PhDs, but here it is. Pardon me if it is incoherent, I don't have time right now to edit.
All professors are, by the very nature, odd. Only somebody seriously committed and interested, some might say obsessed, with a narrow topic of inquiry can complete a dissertation because dissertations are intellectual obsessions with esoteric topics. Often this odd nature manifests itself as the eccentric, slightly absented-minded, and sympathetic professor. Thus, we have the stereotypical professor. In a few, it manifests itself as a superiority over others because of their superior commitment to their field of inquiry and knowledge more generally. The condescending ivory tower elite stereotype. These are two ideal extremes of a spectrum that do not exist exactly in any particular professor. The academic culture only exacerbates the worst among professors and pushes them toward the condescending ivory tower elite type.
Academia is an odd hierarchy setup by odd people. The goal is the number published articles in obscure journals about esoteric topics. Office politics and tenure at a university makes vying for partner at a law firm look like beanbag. Part of this results from the low pay of professors. Don't get my wrong, a full professor at a major university makes a good living, but not as good as a lawyer of a similar age. Add to this that law school is three years, an MBA is two, and the average PhD takes at least four, and you've arrived at a situation with a bunch of people not getting paid as well as other people with less education. The academy does have other perks, like a job for life, sabbaticals, and summers off -- if you make tenure. I've digressed. The hierarchy forces most professors to narrow their expertise even more. They become the expert on the mating habits of the California newt, 4th millennium BC Mesopotamian architecture, 20th century migrant workers in Yuma, Arizona, or 17th century German erotica. The difficulty of getting published and tenure seems like it should make people humble, and sometimes it does. However, it also has the tendency to make people unbearable assholes who think because they know a lot about some narrow field and have a PhD that they are better than other people.
What people dislike about professors is that they have a tendency to either talk down to or over the heads of average people. These average people resent that the person talking down to them doesn't have to worry about quotidian things, like losing their job. Furthermore, the average people don't understand why a person who studies Roman poetry seems to have such an easy time when they are working their ass off doing something useful. So, yes Withywindle is correct -- "they value, and embody, the values of the education status hierarchy more purely than their more powerful peers."
Now, don't get me wrong on this either. Academic inquiry in all fields is tremendously important, and professors have a tremendous amount of insight and knowledge to share with the world. The issue I have is with professors who think that their superior knowledge of a field makes them a better, more worthy person than somebody else. The academic culture skews their perspective of the relative importance of things inside the academy. The most annoying professor is the one who feels compelled to pontificate on all subjects, even ones outside their area of expertise.