The problem, for many people, is that CBS just doesn't want to air the ad during the SuperBowl. It's a great opportunity to show an ad, and MoveOn.org was raising money to be able to pay for the ad time, just like everybody else. But they won't be airing it: CBS considers the ad to be "advocacy advertising," which they have a policy of refusing to air. It's not that it's controversial, it's not that it's crude or offensive, it's not that it's biased in favor of a particular "side" of something. They'll run things in any of those categories without a problem -- unless it's "for" or "against" ... hmmm. I'm not sure that's the best way for them to explain their policy, as they likely feel free to refuse to air ads for particular companies (but not their competitors) as well as "public service announcements" which vary in intent (and bias) based on the current administration. All ads are advocacy ads, on some level. But it really doesn't matter -- they could refuse to air the ads anyway.
There are laws that require businesses to offer equal services to everybody, without discriminating on the basis of age, sex, etc. The laws do not, however, say that businesses are required to provide services to you without discriminating on the basis of other factors, like what's in the ad you're wanting displayed on their bill-boards or through their equipment.
CBS is free to refuse to play this ad. It may not look good for them (at the moment) but they're entitled to make that decision. It's not censorship, and it doesn't hurt free speech. Free speech rights never included a clause forcing people to listen to you, or messengers to carry your message. ("Common carrier" status, as used by phone companies and internet service providers, exempts the carrier from liability for the content being sent through the equipment, as they neither monitor not filter the content for acceptability or legality. This is not the case for a broadcasting companies.) The fact that CBS (or rather, Viacom) controls a large portion of the available broadcasting spectrum does not mean this is censorship. They are not preventing anyone from airing the ad elsewhere, like the MoveOn.org website itself. They are not required to be fair or balanced, nor to cater to all sides of any and all debates (their journalistic ethics might compel them to do so, but it's not a requirement.)
CBS is not a monopoly, and certainly not an unremovable one. If there were only one way to broadcast a message, and no way to create new competitive ways, then maybe there would be a case, somewhere, because it'd be the government's fault somehow. (Even then, that's not entirely guaranteed.) Corporations aren't required to provide the services you want, the products you want, or the prices you want. Industries, as a whole, are expected to "follow the money" and therefore accidentally give you those things -- but it's not required, nor always the case. There are untapped markets, there are unfair prices, there are inefficiencies. Nothing about the capitalist system is guaranteed to be perfect -- only to maybe head that direction, progressing slowly.
The only grounds on which we could complain would be the use of FCC-regulated radio frequencies, which are (partially artificially) kept scarce. But really, that'd be like complaining that a website refused to air your views, thanks to the fact that the website has one of a limited number of IP addresses on a shared, semi-public network.
It's unfortunate that more people won't see this ad thanks to the super-bowl advertising extravaganza. I urge people to go watch it, it's not bad. But there are plenty of other ways to get a message out than the super-bowl, and corporations have the right (currently) to refuse service on this basis. Stop crying, pick up your ad, and go find someone else to air it.