In favor of Rails:
-There are pre-existing FOSS social network apps in rails you can modify.
-You have infinite scalability where your only multiplier is hosting cost b/c there are no windows licenses, so no obstacles to moving into the cloud, virtualizing, setting up a friend
-With rails, you are mostly saved from SQL. Castle's activerecord might do this on .net, but was lousy when I tried it a while ago. Might be better now.
-It is easy to be coddled by ASP.NET and not understand the parts underneath, which works well until the abstraction leaks (viewstate, page layout, etc).
That said, asp.net is not a bad option, and would be my second choice over the java frameworks I've tried, or php. .NET has a nice IDE and better tooling than Rails.