To start, Iraqis now face the reality that part of their country's infrastructure is now unusable. Bridges, roads and missing traffic lights are being slowly reconstructed. Traffic in Baghdad is recognized as being a real hell. Someone quoted in the article even claims that under Hussein's rule traffic was smooth. Add in the rising cost of gasoline, which has been going up steadily and the fact that a scooter costs significantly less than a car (and don't forget that scooters show that you are not likely to be carrying a bomb), and we can see why the two-wheelers are growing in popularity. Most scooters sold in Iraq are imported from China, although Japanese brands are considered more reliable and desirable.
So, besides the security considerations, it's the cost of cars, traffic conditions and the price of fuel that is driving Iraqis to buy scooters, just like the rest of us.
[Source: NYT (h/t to Sayyad for the tip)]