domesticate, raise, keep, feed
飼 centers on providing care and sustenance to animals: domesticating, raising, keeping, and feeding them.
飼 combines 飠 (food/eat) with 司, which likely contributes the sound and the idea of managing or overseeing, together suggesting feeding and caring for animals.
The left side 飠 means food or eating, and the right side 司 looks like a person managing something. Picture a person giving food to an animal to raise and keep it.
For シ, imagine a sheep (シ sounds like 'she') being fed and raised: sheep -> シ, and the sheep is kept well-fed.
to keep (a pet or other animal); to have; to own; to raise; to rear; to feed
(pet) owner; keeper
breeding; raising; rearing; keeping
fodder; feed
pet dog
free-range rearing; letting (animals) roam freely; pasturing; grazing
rearing from infancy
cormorant fishing
breeding; raising
raising (of animals); rearing; keeping
keeping a domestic animal beyond its useful life
fodder
cage feeding
battery rearing; battery raising; battery farming
floor feeding
keeping (a pet) outdoors
owning multiple animals (esp. pets of the same kind)
large-scale breeding
animal hoarding; compulsive accumulation of pets
keeping (a pet) indoors