A dog or cat seems like a great gift, but if an individual is not ready for the pet or does choose them, they have a very high chance of not being the right fit. Even if someone tells you they want a dog or cat, I would still generally say this is a bad idea. Different breeds and personalities tug on us in different ways and the decision to add a pet to one’s family is something that has ramifications for ten to twenty years. In summary, as nice as the idea is, I think it is a bad idea.
However, when thinking about this, I started wondering why people who give pets as gifts do not give rescue animals. Surely, this happens some, but I have not read about it often. I wonder what percent of pets that are bought as gifts are rescue animals. Using this line of logic, I have a suggestion for you if you are intent on giving a pet for someone for the holidays. Although I do not recommend doing so, if you are sure you want to proceed then why not give a donation to a local shelter or rescue to cover the adoption fee for a rescue animal. You can then spend time with the gift recipient over the next month or year or two years finding the pet that works for them best. If they end up deciding against adding a pet to their family, the money will have been a worthwhile donation to the rescue. The reason I would not recommend this is that the individual may just take a rescue animal because they feel obligated to after the gift when they did not really want him or her in the first place. You know your situation better than I do, so take all of this with a grain of salt. I think giving a pet as a gift is a bad idea, but if you are 110% sure you are making the right decision and I cannot dissuade you then think if the rescue idea may make more sense for your individual situation.