Can moths hurt you

No, butterflies and the vast majority of other insects cannot feel pain. Humans and higher animals have special nerve cells that sense pain (called "nociceptors"), but insects and many other invertebrates don't have these cells and therefore don't experience pain.

Insects do, however, sense restriction of freedom. If an insect suffers and injury that restricts its movement, it will struggle frantically. But if the injury doesn't cause restriction, the bug will calmly limp or fly away without showing signs of pain.