Would it be character? Shared values? A commitment to marriage? A good role model for any future sons?
Well, now we know the answer. A reader sent me a link to a story about Helen Fraser who runs the Girls' Day School Trust in the UK:
Helen Fraser, 63, the chief executive of the Girls' Day School Trust, told its annual conference that girls should learn to be just as "ambitious" in their relationships as they are in their careers.
She said that female pupils must learn to find a man that not only helps around the home but would also be a "cheerleader" for their career.
The former managing director of Penguin Books said that girls can have it all - career, marriage and motherhood - but they must learn to pick the right partner to accomplish it.
She said that failure to do so could mean women not so much hitting the "glass ceiling" as being blocked by a "nappy wall" caused by having to make a decision between children and career.
"Just as I believe we should always encourage our girls to aspire to the best universities, I believe we should encourage our girls to be ambitious in their relationships," she said.
She said that she had been intrigued by comments made by the Facebook’s Chief Operating Officer, Sheryl Sandberg’s that “The most important career choice you’ll make is who you marry”.
"Is this what we should be making space for our girls to learn?" she suggested.
Speaking at the GDST's 140th annual conference in London, she said: "It's not just about finding a husband who does the Hoovering and makes the dinner.
"It's about finding one who really understands it is important for you to thrive and do well in whatever you choose to do.
"They should be cheerleaders and take pride in their wife's career as they do in their own."
Here are some of the things that struck me about Helen Fraser's advice to girls:
1. We still have the attitude, one that was expressed so frequently back in the 1990s, that the role of men in life is to enable the autonomy of women. Men are there to prop up women doing well in "whatever you choose to do".
Not only is that a dubious proposition in itself, there is no mention of any reciprocal arrangement. There is nothing about a wife being a cheerleader for a man doing whatever he chooses to do.
It's not surprising that many of the comments following the story in the Telegraph complained of a culture of female entitlement.
2. Clearly for feminists like Helen Fraser the one big good in life is career. A woman's life is to be organised around career goals. Children are to be looked on as a possible threat to career - as a potential "nappy wall". Husbands are to be chosen on the basis of how they enhance a woman's career.
It strikes me as mercenary, though I have to recognise that there is a social class (the more ambitious professionals, e.g. lawyers, business majors etc) for whom career ambition is a central focus in life.
3. Can it work? Only in a haphazard way, in my opinion. Some men might be willing to marry a career ambitious woman because they want the social prestige brought by the income. And some ambitious men might like to see the same career ambition in their wives.
But a lot of men and women are influenced by hypergamy: the man wants to be the masculine provider and protector and the woman wants a man who she can, in some way, look up to. There are men, too, who would find a "career at all costs" attitude in a woman unappealing; other men will be looking for a woman with the kind of qualities and values which would make her prioritise being a good mother for their children.
And there will be men, faced with female peers they can't keep up with in the workplace, who will downscale their own work commitments. They might start thinking of working in more fun, creative fields rather than in steady, well-paid jobs. They might keep studying longer than they would otherwise have done. They might not stick at jobs for long periods of time.
So it's unlikely that Helen Fraser's view of the ideal family life - of two highly motivated careerists, with the husband playing the additional role of career helpmeet to his wife by taking over parts of the mothering role - will ever become the generally applicable one in society.