The reason it isn't safe to pump gas while the car is running is because the car uses a spark to keep running. Although it's rare, that spark can ignite a fire from the gas fumes. This is also the reason you may see stickers on gas pumps telling you touch something metal before you pump gas due to static electricity. Again, it's rare, but that tiny spark can really cause a major headache!
From my own knowledge and experience the reason it is not safe to pump gas while a car is running is because there is a risk of an explosion. When you pump gas there are not only combustible fuels going into your car but a lot of combustible vapors are produced. To minimize the risk of anything catching fire or worse, exploding, you should always turn the car off while pumping gas.
It's safe. In the old days when cars had distributors there was a rare possibility of an explosion. Think about a busy gas station.... All the cars driving in, out, around.... No explosions. There are no sparks outside the combustion chamber to ignite the fumes. I'd be more worried about static electricity or being hit by another car when pumping gas.
What ever you do please don't actually leave your car on by pumping. It is very wrong. And if you really want a huge team of firefighters on your back waiting for you to pump. Sorry but please do not actually do that. Or else your day will be ruined. As well your money.
There is nothing wrong with leaving you car running while pumping gas except for the fact that your vehicle wont know how much fuel is in your tank. There is no risk of explosions because there are no sparks outside of the combustion chamber if there was a risk of an explosion then how would vehicles be allowed to be on at all when they drive up to the pump? Use your head people. People who dont know anything about cars shouldnt be giving advice on them at all.