The most accurate summary of "Minerva and Arachne" is:
Arachne boasts that she is a better weaver than the Roman goddess Minerva. Minerva dresses as an old woman, intent on scolding Arachne for being so disrespectful to a goddess. Realizing Arachne is, indeed, a superior weaver, the furious Minerva turns the girl into the first spider.