The reason everyone wants to describe our current unemployment situation as cyclical just might be because 'cyclical unemployment' is cause agnostic. Cyclical unemployment is defined as just "the deviation of unemployment from its natural rate."
Since it is just a variation, we need not look too hard for causes, it will go away.
Sandra Pianalta, Chairman of the Cleveland Fed, and a member of the FOMC, is on record as saying that unemployment is cyclical:
Pianalto: I still believe that our current high unemployment is a cyclical problem and not a structural one. There's been a longstanding relationship between the amount of growth in the economy and the improvement that it translates into in terms of job creation. We've had a very weak recovery that hasn't created a lot of jobs. So the slow pace of this recovery is causing that unemployment rate to move down more slowly than we'd like.
I'm reassured that this issue is cyclical and not structural when I look at job openings. Prior to the recession, there were two individuals looking for every job that was open, so it was a 2-for-1 ratio. During this recession, that number has jumped to four people looking for every one job opening. So we just have a very slow pace of job openings, which, again, is cyclical, in my thinking.