I don't get it, why is a fan more efficient pulling through a duct or restriction, rather than pushing?
It follows from a mass flow perspective, that higher pressure air has higher density and when you push the air in the duct will have higher pressure than if you were pulling. This means that for a given unit of time, more air flows though a pushed duct than a pulled one. It also means that the fan has to work harder to push against a higher pressure.
When you are trying to get rid of odors then it is better to pull since the inside of duct will be at lower pressure than ambient, so any small leaks will let in more fresh air rather than blow out the stuff you are trying to get rid of and the fan won't be working against as much back pressure.
Obviously this is a huge over simplification, for more information look up Bernoulli's and Boyle's laws.