Germanic languages like English inherit a distinction between eating (of people) and eating (of animals). German has two verbs, essen and fressen, that make precisely this distinction. To say that Er frisst es instead of Er isst es 'He eats it' is an insult, implying he's eating like an animal.
English has lost the special verb, but has adapted the causative feed 'cause to eat, provide nourishment' to work with both senses, and its Zero-suffix nominalization feed to refer to food intended for animals. It appears in several fixed phrases: a Seed and Feed store sells food for animals plus seeds and gardening stuff; if you are off your feed then you have little appetite and are behaving like a sick animal; a good feed is a banquet where everyone eats too much.
And as The English Chicken has pointed out, pets are honorary humans and they get treated like humans in our language, with pronouns like he and she (never it), and this is just another reflection of that fact.