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It's not safe for them to be around the area at the moment = something wrong with them being there right now
Have you ever stood close to your dog and watched them as they ate. Some untrained dogs may growl or snap at you, while other dogs may refuse to eat until you leave or will take their food to another location, probably their cage. Why? Because it’s uncomfortable and they feel like you’re intruding on their meal time or may even think you’re trying to steal their food from them. So if a dog realizes there’s something why can’t a human.
A well trained dog will understand that your food is your food and his food is his food >

Dogs don't really understand it because we give them their food, so in their logic we can provide them with any food we have at hand. Even if we don't eat the same thing dogs are scavengers that rely on humans for getting food. Begging is a normal behaviour because it's part of the "seeking for food" process.
But their food is their food. It's their resource, and when they feel it is endangered they try to protect it. Since dogs are not pack animals, they don't share, they might even try to steal other dog's food. >

There is something wrong with begging. Sometimes the pant and get their hot stinky breathe on your food. Sometimes it’s dangerous and it’s also just rude to other people. 
Having a well trained dog is good but it makes your argument invalid because the sheer act of sending them away means your acknowledging the fact that it’s bad. >

Why is your dog 2 inches from your food and therefore capable of breathing on it? The only instance I can see this is possible is if they’re standing an inch from the plate whilst you eat. Why are you eating on the floor or why is the dog at the table?
And the act of sending them away doesn’t = bad. It just means it’s not safe for them to be around the area at that moment.
I don’t care if my dog watches me cook, the same way I don’t care if my son watches me cook, however I send them both away when I carry hot water from the stove to the sink.