Raising a pet takes time, as does getting him situated into a new family. And the time between Christmas and the new year often involves a lot of traveling and time away from home. Leaving a new puppy or kitten behind while you go visit the in-laws can cause undue stress and anxiety, leading to health problems and plenty of accidents on the carpet or claw marks on the couch. Remember, once Christmas is over, that new pet isn't going to train himself, and he'll still need attention when the last ornament is packed away.
Pets can be a wonderful addition to a family. Just not when they're gifted to an unsuspecting recipient.