Yes, it is Arachne's pride that caused her downfall. She failed to acknowledge the source of her talents, the Goddess of crafts and wisdom - Athena that she even challenged her. She boasted about her greatness with no one teaching her to be that great. Such demeanor prompted the Goddess to intervene but still Arachne prided herself for such talents that she didn't care whether she offended the Goddess or not. She is too full of herself that she forgot she is only a mortal and she is fighting with a Goddess.