A cat arching its back and rubbing against people can be caused by a variety of reasons. Here are some possible explanations:
Marking territory: Cats have a strong sense of territory, and they mark their territory by rubbing against people. When a cat rubs against someone, it transfers its scent to its owner, which is not only a way of marking territory but also an expression of belonging and dependence.
Expressing friendliness: Cats are social animals, and they will rub against people to express friendliness and affection to their owners. When a cat likes you and wants you to be its friend, rubbing against you is a great way to communicate.

Seeking attention: Cats are social animals that crave interaction with their owners. When cats feel lonely or bored, they may try to attract their owner's attention by arching their back and rubbing against them, hoping that their owner will play with them or give them more attention.
Pain or discomfort: Cats may also arch their backs if they have abdominal pain, spinal pain, or other physical discomfort. If your cat continues to arch its back for an extended period, it is recommended to take it to a veterinarian as soon as possible to determine if there is a health problem.