Bad logic and flawed data extrapolation in the title and graph. You can't extrapolate percentages linearly over large amounts, otherwise by the year 2550 there will be 125% unemployment. As usual, relevant XKCD: https://xkcd.com/605/
I don't think the findings are all the flawed -- you see similar %'s in other developed economies. It's not like Lawrence Summers just extrapolated the data and relied only on that!
I edited my comment to say title and post. After reading a bit more thoroughly I realized he doesn't blindly use the graph data. But that title on the post is sure misleading! I guess the article title "A disaster is looming for American men" was a bit too vague for HN, but I think the replacement title is flawed.
Why American men specifically? Is it that women tend to be in careers that are less under threat in the next 34 years? Or, are they similarly affected here?
women's role in the economy (not seeking employment -> seeking employment) has shifted drastically over the decades, making it harder to draw silly linear trend lines like OP.
I really wonder what people will work with in the future with both the AI and human population advancing rapidly.
Jobs will be taken over by robots at the same time as more mouths will have to be fed.
More mouths will be fed. The robots will still do the work for humans, in fact a lot more work. The questions is how to best distribute the wealth instead of concentrating it.