One aspect of the Egyptian demonstrations clearly goes against the government's favored narrative: that the only alternative to the regime is the Muslim Brotherhood, and we don't want that, do we? This is the usual response to calls for lifting the State of Emergency, democratization (look what happened in Gaza!) etc.
Watch the videos now all over YouTube and Facebook. Do you see any beards? Well, maybe a few beard-and-mustache looks of some young hipsters, but not the beard-without-mustache "uniform" we associate with the Muslim Brothers. Where was the Brotherhood? (Where is Husni Mubarak, of course, is the other question.)
The Brotherhood's English and Arabic websites have been reporting the events closely, and the MB issued a cautious statement that its membership could participate as long as they were peaceful and obeyed the law. But this is clearly a movement of young, secular, middle class Egyptians, or those who would be middle class if they could find jobs.
The Brotherhood may have calculated that their presence would hurt the protests (the absence of Islamists from the Tunisian revolution has been remarked upon), or they may just figure they'll be rounded up anyway and they might as well not make it worse. But it does go against the narrative, encouraged by the regime and by some others, that the only alternative to autocracy is political Islam. And when the regime tried to blame the MB anyway, they made themselves look ridiculous.
One of the spurs to the present demonstrations, along with Tunisia, is the New Year's bombing of the Coptic church in Alexandria, which has led to much popular feeling about the dangers of religious polarization. That may be another reason for the Brotherhood sitting this one out.