A wolf accustomed to moving his own cubs can, if necessary, mouth an egg without breaking it, and though Father Wolf's jaws closed right on the child's back not a tooth even scratched the skin, as he laid it down among the cubs. (1.29)
The wolves are surprisingly gentle to those they consider family.
"He is our brother in all but blood," Akela went on. (1.126)
Akela talks big about Mowgli being brother to the wolves, but most of the other wolves aren't buying it.
"I do not call ye my brothers any more, but sag [dogs], as a man should." (1.130)
Mowgli is so offended when his own brothers want to kick him out of the pack that he refuses to acknowledge both their family connection, and even their species, calling them lowly dogs.
"Come soon," said Mother Wolf, "little naked son of mine; for, listen, child of man, I loved thee more than ever I loved my cubs." (1.144)
Wow, Mother Wolf, don't let your wolf children hear that—they already want Mowgli out of the pack.
"Those feet have never worn shoes, but thou art very like my Nathoo, and thou shalt be my son." (5.12)
Messua is the only human family Mowgli knows, and she only takes him in because she lost a son who looks just like Mowgli. (Could Mowgli be her long-lost son?)
"I can't help that," said Matkah; "there's going to be [a white seal] now"; and she sang the low, crooning seal-song that all the mother seals sing to their babies. (7.18)
Even though Kotick is white, unlike any other seal, Matkah loves him just as she would any of her other cuddly little seal babies.
Matkah, [Kotick's] mother, begged him to marry and settle down, for he was […] a full-grown sea-catch, with a curly white mane on his shoulders, as heavy, as big, and as fierce as his father. (7.70)
Kotick's mom wants him to start a family of his own, but Kotick knows there's no point in starting a family if they're not safe. He needs to find a beach safe from seal clubbing before he brings any new seals into the world.
"I don't like that," said Teddy's mother; "he may bite the child." "He'll do no such thing," said the father. "Teddy's safer with that little beast than if he had a bloodhound to watch him." (9.15)
By showing that he trusts Rikki-tikki, the father is welcoming the mongoose into the family.
"He is Toomai, my son, Sahib," said Big Toomai, scowling. "He is a very bad boy, and he will end in a jail, Sahib." (11.29)
Big Toomai's parenting technique is twofold. He disparages his son to others and to his son's face (earlier he calls him "little worthless" (11.15)) in order to discourage Little Toomai from acting special. He wants his boy to fly under the radar.
"Never you mind my family on my father's side," said Billy angrily, for every mule hates to be reminded that his father was a donkey. (13.67)
This is both a funny line, and ironic considering almost every other character in the book wants to be part of a family, yet the mule wants to set himself apart from his heritage.