Aggression is not an uncommon emotion in cats, & is displayed both by pet cats and kittens. That is why all pet owners should know how to handle aggression in cats. They must be particularly wary of alpha cats, which are the top cats in their pack and display leadership qualities.
These cats use aggression as arm twisting tactics to obtain sure benefits for themselves in preference to other cats. They will therefore turn aggressive over baths, food, toys, space and competition from other cats forcing owners to let them have their way
They may also use aggression as a way to getaway an action. For instance, an alpha cat may jump onto your lap when it wishes to be petted; however, once it tires of the activity it may resort to scratching and even biting to get you to stop. This phenomenon is termed as petting-induced aggression, and it is common in cats that have a low threshold for physical affection. This is also a way for these aggressive cats to show who is in control.
Surprisingly, kittens, though young, also show a high degree of aggression. Aggression in kittens is in fact a biological phenomenon and is termed as play-aggression, that is an in-built drive to play rough. Play-aggression mostly occurs when your kitten is beginning to grow up into an adult cat and is 'practicing' its survival preparations. Fortunately, it is a phase that most kittens outgrow.
It is important to deal with aggression in a firm manner. If an alpha cat bites you when you are petting it on your lap, you should make it a point to show your disapproval by not allowing it to get back on your lap for a few days. When it does get the privilege of sitting on your lap, ensure that you are in control and in charge of petting activity. You must initiate as well as conclude the petting session. After a few days, the cat will learn to accept your role as its owner and may also learn to be patient.
In the case of kittens, it is you who needs to be patient. Besides that, you could learn to read your kitty's body language and not give it a chance to 'attack' you. You could also get it another kitten as a playmate.