Why does the family decide to let Rikki-tikki stay in its home?

The narrator of the story is not explicit about the family's reasons for keeping Rikki-tikki-tavi in its home, but the family's tender treatment of him reflects a subtext of compassion and love for animals.
First of all, the boy who finds Rikki-tikki-tavi wants to have a funeral for him, believing him to be dead and wishing to respect Rikki-tikki even in death. Then the mother wants to take the mongoose inside and dry him to give him a chance at life if such a chance exists. Lastly, the family wraps Rikki-tikki-tavi in cotton wool to warm him and place him next to the fire, hoping he will revive. All of these behaviors reflect the family's genuine interest in taking care of animals, especially animals like Rikki-tikki-tavi who are in need of help.