Why does athena turn arachne into a spider instead of saving her life or just letting her die?

Metis wanted nothing to do with Zeus and tried to escape as best she could, going so far as to change her form many times, turning into various creatures such as hawks, fish, ... Athena railed against excesses in war or everyday life ... that it doesn't pay to compare themselves to the gods, she changed Arachne into a spider.