Arachne was the attention in her village everyone wanted to see her sew
Arachne said she was equal to the gods and a old lady that turned out the be the goddess Athena said to not claim that she was equal to the gods. They also agreed to a competition.
I am equal to the gods
You should not consider yourself equal to the gods
Arachne was losing in the competition to Athena.
Arachne had lost the competition and had tried to kill herself but before she could Athena turned Arachne into a spider Arachne's act of hubris and self pride was what made her consequences be her turning into a spider.
This could be a lesson to modern day children to not boast about their accomplishments and skill because there might be consequences.