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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
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.