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.
In general gases consisting of single atoms, i.e., the noble gases are much poorer heat conductors than molecular gases. The reason is that if a molecule hits another molecule or a hot wall its internal states, usually vibrations, can get excited. In other words, they pick up a little energy and if they then encounter another molecule or a cold wall, this energy can then be transferred to the other molecule or the cold wall.
This mechanism does not exist for noble gases and that is why noble gases are preferably used for double glass windows. In that case energy can only be transferred by a change in velocity during collisions. Air, which consists of nitrogen and oxygen is less well behaved. In particular the water vapour in wet air can spoil the insulation properties.
In general, the more complicated the molecules, the more vibrational degrees of freedom they possess, so the more energy they can pick up. This possibility of picking up energy plays an important role of global heating.
Best Answer
No, conduction and radiation are two different ways how to transfer heat. During radiation, an atom emits energy in form of a photon that gets absorbed by another atom and heats it up. But during conduction, the atoms exchange energy in collisions. So conduction and radiation are two completely different mechanisms.