"ungodly stories and old wives' tales." "Profane" here refers to stories that purposely dishonor God. Translate "stories" as you did in [1 Timothy 1:4](../01/04.md).
This is probably an expression that means "silly" or "absurd." Paul is not purposely insulting women in his reference to "old women." Instead, he and his audience knew that men die younger than women, so there are more women than men whose minds have become feeble due to old age. (See: [[rc://en/ta/man/jit/figs-metaphor]])