The question comes from Quora. It is a disturbing but fiercely honest question as the person who asked it has admitted to the world their error (but they remained anonymous in terms of their name). And it is a grave error as what they did has clearly damaged the relationship. I hate to say it but I sense that the cat’s owner is unsuited to the task of looking after a domestic cat.
So the first possible advice is to rehome the cat and give up any ideas of having a cat in the furture. Hiting a cat hard, as described, is a crime. It is a crime in any country where ther are decent animal welfare laws. So the person has in fact admitted to a crime; probably a misdemeanour crime. They are apparently unaware of that. Another reason for them to give up being a cat owner.
A cornerstone of cat guardianship is to never punish a cat. Punishment is the opposite to positive reinforcement which is a way of training out what some consider to be poor behavior but which is often normal feline behavior. Positive reinforcement should always be employed.
If this person retains their cat the only way forward is months of TLC and gentle, friendly interactions with him who should forget the bad experience of being hit. They might not though. Also it is perhaps possible that the person has created a hostile environment for their cat as this single action may not be entirely unique. They have a new kitten. This does not look good. Tip for delivering TLC: get a good quality flea comb and gently comb the top of his head with it. He should love it. Then progress to combing the neck, shoulders and the base of the spine. It’s a great way to (1) flea comb and (2) bond.
We should also ask what their cat was doing when he bit the new kitten. What was happening? Was it a hostile bite? Was it a play bite? Are the cats friendly with each other? Or was her cat aggressive towards the kitten because he regarded the kitten as an intruder into his established space?
If the latter is the reason the cause is the person who hit the cat. He or she introduced the new kitten into the resident cat’s territory (home range). They should take responsibility for the cat bite. You have to introduce a new cat with patience, care and consideration. Pretty well everyone knows that. You can’t assume that a resident cat will accept a newcomer. We never expect a person to accept a newcomer into the house. We wouldn’t consider doing it. The same applies to a cat. I don’t believe that enough cat owners take sufficient care when bring a new cat into the home of a resident cat.