Sometimes I offer her food and she shakes her head. It means "no". If I continue to offer her the food she pushes it away, shakes her head again and then turns away from the food. It clearly means "no". Which makes sense. A shake of the head always means "no".
In most people.
Other times I offer her food and she shakes her head. Then opens her mouth and lunges towards said food. She heartily eats it. Clearly, the head shake did not mean "no". Did it mean "yes"? Did it mean "no, oh alright then, you've twisted my arm"? Or did it mean "I don't really know. But as it's there I may as well"? I really have no idea.
A colleague told me a story about his two year old son who will have a tantrum at the dinner table demanding a biscuit but when one is offered to him he pushes it away and yells "no biscuit".
Children are very confusing
Sometimes Phoebe shakes her head and there is no food anywhere to be seen. She smiles and seems to be doing it just for the fun of it. Perhaps she just likes the sensation. Maybe it's "just a phase".