That was actually a sign of affection, believe it or not. Feline pokémon, especially basic-stage or “baby”-like ones such as litten, will show affection by nibbling their trainer’s hand gently. It has to do with how felines interact with each other. Play-fighting is an important part of cat pokémon development, and they’ll often engage in roughhousing with one another to develop important skills, such as pouncing, clawing, and—of course—biting. Biting then translates into other forms of affection, especially if someone who is very decidedly not a cat gives them a limb for them to “capture” and nibble into. Thus, if your feline pokémon does this, this is a sign that they’re excited and, yes, would like to show you that they consider you a part of their families.
(However, note that if your feline pokémon pushes you away after a nip, this means they would like to be left alone. Always read your pokémon’s body language to ensure that you’re translating their signals correctly.)
As for why it decreased as your litten grew older, the answer is actually equally simple: love bites would hurt you. As a litten evolves, it gains an affinity for the dark type, and with it, it gains an understanding of what using it means. So once it reaches the torracat and incineroar stages, it realizes that it can’t display affection the same way, as this would harm you, a strange incineroar without any of its abilities or resistances, more than help you understand what it’s feeling. So instead, it resorts to other means of affection and only uses “love bites” if it thinks its message isn’t getting across (or if you’ve accidentally trained it to show this form of affection above anything else).
By contrast, it should perhaps be noted that this behavior lingers a little longer in both forms of persian, but that’s mostly because both forms of persian are a little more sadistic than most feline pokémon. Thus, if your persian grabs your arm with a paw, try to gently pull yourself away without getting clawed.
Best of luck!