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The point of the article is not that men should not be ambitious, but that their self-image should not rely on how much money they make. You might consider it "ambitious" if a woman spends a significant amount of time, money, and effort on her appearance in order to look like a celebrity or supermodel, but others would call it "dumb and dangerous."
But a woman's image of that man will often depend a great deal on how much money he has. Not all the time, and it's not the only factor, of course, but to say it's not a big or frequent factor in the real world is to deny reality. (Not assuming you think that, more that the OA's message came close to making this mistake.)