Why did the religion of the ancient Egyptians have a cult of a cat, a scarab?

Because these beings were sacred. The scarab beetle was a symbol of the god Ra. it was believed that the beetle rolls the sun along the heavenly slope. At the same time, kosha in Egypt was a symbol of fertility and sunshine. The cat goddess was Bastet. She personified the patroness of fertility, joy, fun, prosperity and home. Most often she was portrayed with a female body and a cat’s head.