But the point is that, if where you ended up was completely unrelated to where you started, you would expect 20% of the middle fifth to end up at the bottom, 20

But the point is that, if where you ended up was completely unrelated to where you started, you would expect 20% of the middle fifth to end up at the bottom, 20% the 2nd lowest fifth, 20% the middle, 20% the 2nd highest, and 20% the highest. The article seems to be arguing there is NOT a lot of social mobility, but if so you wouldn't expect more than 20% of the middle fifth to end up in the top.