The answer to this question is quite straightforward. Your cat is treating your arm as prey. When prey tries to escape a cat hangs on harder, digging her claws into the prey item so that she does not lose it. She will also bite on it as an act of killing prey. Struggling to remove the arm makes it worse as a cat will tighten her grip. The human response should be passive and still plus distracting the cat (wave the other hand around at a safe distance). Then you can release your arm and hand slowly.
So why should a cat treat a person’s arm as prey? Well once again most enlightened and educated cat owners know the answer. Domestic cats play-hunt. When they play they are hunting. So if you play with your cat using your arm and hand she will treat your arm as prey.
You might not deliberately use your arm and/or hand as prey but your cat might see it as prey because it is near her and because perhaps you are stimulating a play-hunt response. The classic moment when this happens is when a cat owner is stroking her cat too strongly or on the belly for instance. Stroking too vigourously can provoke the play-hunt response.
That’s the answer. As I said at the beginning, the answer is straightforward. The way to avoid it is to avoid getting to the point where your cat thinks that your arm or hand is prey. Sometimes domestic cats see ankles and feet as prey or the lower part of a person’s leg. This is because it’s moving near them and if they are perhaps immature they will target it and jump on it. They should learn to stop doing this. It can be trained out.
Cat caretakers should realise that they are living with a top-flight predator whose major motivation is to hunt and kill. That is an underlying driving force for the domestic cat and it must always be respected.