I think “Failure to Privilege”—caps and all—carries an ironic twist that goes a little bit beyond the interpretations already given here. It would be best to see it in context (if there is one), to judge where the main emphasis is supposed to fall. Lacking that, I tend to see this remark not as a comment on parents and children and affluence but as a comment on privilege itself.
The idea that the son’s reign could be as prosperous as, and even more prosperous than, the father’s and still be considered a failure (by not being prosperous enough) is an idea that you can’t afford unless you’re among the privileged. Just having enough to get by, maybe with a little to spare, is plenty for most of us.
“Failure to Privilege” implies a debt or obligation to the abstract notion of privilege per se and not to a person or society. If you fall short, Privilege itself (given substance by the initial capital letter) will be disappointed in you; you’re not upholding the expectations of your class.
Being among the privileged gives you the right to whine about things that others can’t be concerned about (so goes the logic, at least): much like first-world laments that third-world people would never dream of voicing or even thinking. “They didn’t have my brand of decaf.” “My computer is too slow.” “We’re desperate for a three-car garage.” “I need another closet just for my cashmeres.”
I take the king and prince to be metaphorical—that is, not literally titled royal rulers but any heirs to significant status and fortune. So an heir who fails to increase the bounty that was handed to him is letting his peers down by being a weak link—letting the gap between him and the masses shrink instead of making it grow, and hence threatening the ascendancy of his class. And not only letting his peers down but letting the meaning of privilege lose some of its power.
We’re not doing your homework for you, are we, @partyrock?