These answers are not the only possible ones or even especially good ones. They do, however, provide some direction for the teacher. Cats purr because they're contented. Cats that purr receive more attention from mother and so live longer and have more offspring. Cats purr to show they are feeling friendly.
Dogs sleep on their owners' beds because it's warm.
Survival in dogs is keyed to living in close cooperation with other dogs. There is an advantage to the male lion putting as many offspring into the population as possible. Gorillas, because of their size, can scare away enemies without having to fight. Female gorillas are attracted to strong male gorillas. Gorillas that don't waste energy fighting live longer and produce more offspring.