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."
A man's self-image should not rely on how much money he has.
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.)
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."