Why is my cat biting its nails and pulling them out so hard?
There are two main reasons why cats bite their nails and pull them out forcefully:
1. Self-scratching: Cats' nails grow continuously, and they sharpen their claws by biting and pulling on them. This is a natural behavior that helps keep the nails sharp and of appropriate length.
2. Discomfort or anxiety: Cats may feel discomfort or anxiety when biting their nails and pulling their claws. This could be because the nails are too long or deformed, there are wounds or pain around the nails, or the cat is in a stressful or anxious environment. 
In the first case, this is a common and normal behavior for cats. You can provide suitable scratching toys or durable flooring for your cat to use to help them wear down their nails, and trim their nails regularly.
For the second situation, you can consider the following methods: check if the cat's nails need trimming, avoid stress and anxiety in the cat's life, provide a comfortable and safe environment, avoid stimulating or frightening the cat, and take the cat to the vet for regular health checkups.