Well, the argument is not very well put:
Because the air is a bad conductor of heat the soup stays hot longer: only the first layer of air touching the soup gets hot fast, and heat is not transmitted efficiently to the bulk of air.
For soup, in contrast to thermos, evaporation cooling should also be considered.
Convection by continuously replacing the contacting layer of air increases the heat transfer to the bulk of air by conduction and at the same time the rate of evaporation increases, increasing cooling.
So the soup cools faster than if there were no convection.
If air were a good conductor of heat, the soup would cool fast, as in a metal plate on a metal surface.
You could go through a read of the wiki article.
Edit: Georg's comment makes me add that of course the soup would be also cooling because it will be radiating with the corresponding to its temperature black body spectrum. Convection increases the rate of heat loss over the loss through radiation.
To address the title, which differs from the questions in the content:
Why is air a poor conductor of heat?
It is mainly the very low density of gases that make them bad conductors of heat. In liquids and solids atoms and molecules are densely packed and transfer of energy has much smaller distances to happen. In a gas molecules have to scatter off molecules to exchange energy in larger distances, so the probability of transfer is much smaller.