Don

Here is an insight into Titus that Kenneth Bailey had which I like.

Titus is charged to teach older men, older women (these might be the elders) and younger men, but the older women are charged to teach the younger women, per Titus 2:1-6.  Now WHY might Paul instruct Titus to not directly teach younger women?  I think the answer is because it would be cross-gender to a person of similar age.

A teacher is in authority while teaching (to maintain order).  So to avoid any appearance of impropriety in the 1st century, Titus should avoid directly teaching young women, as he is a young man.  It helps to know that adultery was just assumed when a man was along with 1 or more women, as the Jewish sages taught that they would seduce him.  This last from Instone-Brewer, not Bailey.