Nitpick: I think the agreement here on that claim is limited. Women wanting higher-status men is not some kind of universal immutable truth about women or relationships: it’s basically a historical side effect of traditional patriarchal male supremacism in society.
Of course it’s traditionally been the case in patriarchal societies that when women aren’t allowed or expected to advance themselves socioeconomically as independent economic actors, women tend to focus instead on advancing themselves by marriage with higher-status men. If “marrying up” is your only available career path for fulfilling any personal ambitions you may have for attaining increased wealth, prestige, power, etc., then naturally you’re likely to place high importance on marrying up.
And as usual, social expectations tend to persist—for a while—as cultural stereotypes even when they no longer reflect economic realities. The stereotype of a man needing to out-earn “his woman” in order to be adequately “manly” does still have resonance with many people, men and women alike. But more and more people are questioning and rejecting it, and will continue to do so.
Part of the problem in the meantime, of course, is that socioeconomic changes have made it easier for people to forget just how shitty many aspects of the traditional patriarchal system were for men. As usual, when things change in society, dissatisfied people concentrate on the aspects that got worse and ignore the ones that got better.
A non-high-status man of today, struggling to find lower-status women to date, may feel resentful about women’s increased economic autonomy and decreased incentive to date him. But he’s forgetting that “back in the day”, he might well have been expected to help support other women in his family, not just his wife. Widowed and spinster (or divorced or deserted) mothers, mothers-in-law, aunts, sisters, daughters, orphaned nieces or cousins, chronic invalids in any degree of connection, you name it.
In the era of near-universal female economic dependence, men’s breadwinner status may have made it easier for them to readily attract mates, but it also came with a lot more potential responsibilities to women other than their mates. But, again, these compensatory aspects tend to get overlooked when people get stuck into their grumbling.