From the article...
It’s true that men who have left work to do their thing as full-time parents has doubled in a decade, but the numbers are still minuscule: only 180,000, according to Census data, which University of Maryland Sociologist Philip N. Cohen calculates is only 0.8% of married couples where the stay-at-home father was out of the labor force for a year.
I agree with the general conclusions in this article, but I will note that the writer isn't writing it with any sense of compassion toward the men who choose that path or aren't allowed to choose it. It's strictly written to prove that women still have it harder. She makes that clear in her last paragraph...
stay-at-home fathers may make all the difference for individual families, but their presence won’t make a dent in the numbers of high-potential women who are forced to choose between family and career.
As a working stay-at-home dad who is very sympathetic to the plight of women in our society, I must admit that I'm still irked by the tone of that last sentence. It just sounds like a sighing, "we'll never be able to count on men to do the right thing."
That may not be the best approach to convince men of your point of view. If it irritates me (who agrees with you), I can only imagine how much it irritates someone who doesn't.