Grain is just food that happened to possess two essential features:
Making it was sufficiently productive, that is, a group of humans could grow more grain than they themselves would need;
It could be stored for a long time with only minor spoilage. Having reserves of stored food to survive things like winters, droughts, and plagues of locusts is rather essential for a burgeoning civilization. Besides, without non-perishable food it's hard to have cities.
You left out an important property:
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