My understanding is that in those early agricultural mesopotamian societies the lines between beer, bread, and porridge were very blurry by modern standards. They didn't so much drink beer with meals as drink a thick, sludgy beer
as meals. And that was valued because the malting step increased the availability of the calories.
They also had more familiar-to-us breads, as well as unfermented cooked grain gruels. Again though which of these things you call bread and which beer is a value judgement. Some of the porridges could be drunk and some of the beers thick enough to eat with a spoon.