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.
Three processes are involved:
Conduction: Heat flows from the object to its environment. Removal rate of heat from the interface further away from the object is proportional to the coefficient of conductivity (0.024 for air, 205 for aluminum -see http://www.engineeringtoolbox.com/thermal-conductivity-d_429.html).
Convection: The interface between the object and air is the same, but removal of heat from the interface is by replacing the interface volume, due to the flow of air (e.g: due to wind). Convection is more effective than conduction within the air - hence the familiar habit of blowing on hot food to cool it.
Radiation does not depend on the immediate environment. There is, however, a balance between incoming radiation (from the sun, earth, space etc.) and outgoing radiation (from the object). With very hot objects - radiation heat transfer would be dominant.
Best Answer
A good example would be heating a tin can of water using a Bunsen burner. Initially the flame produces radiation which heats the tin can. The tin can then transfers heat to the water through conduction. The hot water then rises to the top, in the convection process.
The atmosphere would be another example. The atmosphere is heated by radiation from the Sun, the atmosphere exhibits convection as hot air near the equator rises producing winds, and finally there is conduction between air molecules, and small amounts of air-land conduction.