When it was a mixed-sex group, and the person at the head of the table was male, again the students reliably chose him as the leader. But when it was a mixed group, and the person at the head of the table was female, half the time the students chose her as the leader, and half the time they chose a man who was sitting somewhere else at the table. This is a small example of something that happens repeatedly to women. You talk in the book about how there's no one big factor responsible for women's lagging progress, but rather a series of small nicks along the way. What makes it hard to understand women's slow advancement is that nothing seems overtly wrong in most work situations, especially in academia and science, where the meritocratic ethos is so prominent.
People are often unable to perceive or assess how small imbalances can really add up.
The programmers continued the simulation until there had been a complete staff turnover at their fictitious organization. Any single instance of bias is likely to be tiny, and someone might say, you're making a mountain out of a molehill. But mountains are molehills piled one on top of the other. It sounds as though just getting more women into the pool will not necessarily help. In fact, widening the pool of female candidates does help.