They learn to retract their claws and to inhibit their biting as they mature, but until that time, Grandma and Junior can sustain considerable damage. Small children can pose a substantial threat to the health and well- being of the kitten as well. Naturally children want to pick up and hold the only living creature that they've met that is smaller than they are. When the kitten squirms to get away, they squeeze harder to keep the kitten in their arms. The kitten may sustain internal injuries and the child may be bitten or scratched.
Constant supervision is necessary to prevent such tragedies.
Families with small children would be better off selecting an adult, neutered male with a laid-back personality for their family pet. This is an unfortunate misconception because many older pets are already well socialized and have had some good training. Even those who haven't can be very responsive to behavior modification techniques. If you already have a resident cat it is important to take this cat's personality and activity level into consideration before selecting a feline companion. If you are too casual about this important decision, your house may become a war zone.