Conservatives argue (often with comparisons to communist states) that the doctrine, which hasn't been in effect since 1987, forced the state to mandate speech. It really just provides for reasonable discussion of views, but the Right demagogues the issue to raise money and keep Rush Limbaugh on the air unopposed.
But now that McCain can't get his stuff in the Times, it's a terrible moment for American media! The FCC's regulation wouldn't affect a print newspaper, obviously, but it's rank hypocrisy for McCain to complain that he's not getting a fair shot, especially when he is co-sponsoring legislation to permanently ban the Fairness Doctrine. Apparently, equal time is only a bad idea when liberal views are being silenced.
This really isn't complicated: The difference between advocates for bringing back the fairness doctrine and conservative critics of the New York Times is that the conservatives are not (as far as I know) advocating that the government force the New York Times to carry John McCain's op-ed, or even to carry a certain quota of conservative columnists in order to ensure a "reasonable discussion of views."
Fernholz dances around this issue, asserting that it's not really censorship because the goal is simply to promote a "reasonable discussion of views." And it's true, I guess, that the Fairness Doctrine doesn't involve giving the White House veto power over which stories get aired on NPR. But imagine if every five years the New York Times had to get its printing license renewed, and the Federal Press Commission reviewed the previous five year's op-ed pages to ensure that they had represented a "reasonable discussion of views." Fernholz can't seriously claim that this would have no effect on the Times's coverage—that it might not decide to scratch a few op-eds critical of the current administration or maybe hire an extra conservative (or liberal, depending on who was in power) columnist to make sure there weren't any "reasonableness" problems during the license renewal process.
No, conservatives and liberals agree that the publishers of newspapers have a right to print whoever they please on their op-ed pages, "reasonable" or otherwise. The same principle applies to broadcast media, and for the same reasons.