What argument will you employ?

Maturity comes from spanking

"But, Tilly, it's the very threat of spanking which teaches girls the maturity they need to do without spanking when they're older. You say you want to wait until you're ready to take the responsibility of being the boss without corporal punishment, but the quickest way to do that is to learn on the job, getting thrashed whenever you make a mistake."

"Yes, Jack, but I can learn that in my current position. My colleagues certainly aren't hesitant to discipline me when I need it and when I'm old enough, I can apply for a promotion I'm capable of fulfilling without further guidance. In fact, I'll probably learn quicker and be punished more stringently in a more junior post."

This is an unusual situation. Due to the rules you created on the day you found the Rulebook, Matilda ought to believe that she needs guidance from older men, such as you and her father. The fact that she hasn't taken his advice and seems resistant to yours means she must have a very strong reason for declining the promotion. Having attended the university, she can't be a stranger to public punishment and humiliation, so it must be something else deterring her, but neither you nor her parents nor Sharon Blake can work out what it is. If only you could spank her for arguing with you, but having a different opinion's not a punishable offence by itself. You'll need to try a different tack.