Why is a washing machine unable to spin-dry a duvet? Background story: I put my duvet (synthetic filling) into a washing machine, and the machine was unable to spin-dry it. My mom told me: "It's because it is full of air".
I was not satisfied with the answer. So: Why is it problem for a washing machine to spin-dry a synthetic duvet? From my point of view, the only important factor is the momentum of inertia, that depends only on the weight and distribution of the weight.
I do not think that the momentum can be significantly higher for a single duvet than for a large lot of casual clothes.
 A: As noted in the comments, weight must be evenly distributed or the washing machine will spin off center and shut down. 
Clothes are a lot of small pieces. When spinning starts, they fly to the outside. Usually they are uniformly distributed. 
A duvet is a single large piece. It is easy for it to be off center. For example, if you wrap it around the outside, the ends may overlap. When spinning starts, the place where the ends are is not uniform. The ends try to pull the whole duvet over. You may succeed if you carefully arrange the duvet when the spin cycle starts. 
You may also destroy the duvet. Down comforters and sleeping bags are particularly susceptible. They have internal compartments to keep the feathers uniformly distributed. The compartments are made of very thin material to keep comforter or sleeping bag light. They are not strong enough to hold wet feathers against centrifugal force. 
A: The solution has to have with the 'surface tension' of the exterior surface.
Google for 'surface tension' satin water repellent synthetic tissue 
and find:
'Liquid water is prevented by surface tension from penetrating' on Polyester Microfilament Woven Fabrics 
Conclusion : the exterior surface of the duvet (and not the interior material) is blocking the water flow,  much similar to the properties of bird's feathers.   
