Bion was a psychologist who was doing group therapy with groups of neurotics. (Drawing parallels between that and the Internet is left as an exercise for the reader.) The thing that Bion discovered was that the neurotics in his care were, as a group, conspiring to defeat therapy.
Groups have their own logic, and Bion identified three ways that groups can keep themselves from getting anything done: sex talk, hating external enemies, and veneration-- I think that last is equivalent to focusing on internal enemies. Online groups have a fourth failure mode: the raw entropy of spam, flaming, and vandalism. (That last is my deduction-- I don't think Shirky makes it explicit.)
If a group (especially a large group) is to do anything other than the easy defaults, it has to have members who are committed to making it so, and while the software affects whether a core group can take charge, the software can't make good groups happen.
The essay doesn't address what happens if the core group goes bad, but this is hardly Shirky's only essay about social software.
Link thanks to patrissimo.