What argument will you employ?

It will make her parents happy

"I know you're a good girl who loves and respects her parents, Tilly. I also know that they'll be proud of you, whatever you do, but what would make them happiest is for you to take the job. Won't you do it for them, girl?"

She nods, thoughtfully, before replying. "I realize they'd be happy about me getting promoted, but that wouldn't last long if I couldn't cope in the job. I think it's better to delay that pleasure a little while, to make sure it lasts longer. My dad always says to take the long view."

"Surely there's no chance of you not coping," you practically scoff at the idea that a graduate of your university could fail at anything.

"Well, there was another young woman at a different branch, who was promoted before she was thirty. Her subordinates never took her seriously and she couldn't control them. It was really bad and head office had to step in. She's on permanent probation now and she'll never get another management position again. I don't want that to happen to me."

This is interesting information. You probe further and find out more details about what went wrong, but try as you might, you can't convince the shapely brunette that she'll fare any better if she's still of spankable age when she becomes the boss. If the root of the problem lies in the ethos of the company rather than the young lady walking beside you, then your mission may be impossible, but you won't be defeated without a fight.