You're lucky to have such an enlightened workplace. There are many companies where fathers are officially allowed to take parental leave or work flexible hours

You're lucky to have such an enlightened workplace. There are many companies where fathers are officially allowed to take parental leave or work flexible hours, but in practice everybody knows that those are really just for women; the fact that men are allowed to make use of those options and people don't say anything doesn't necessarily mean that they don't quietly write off child-caring men as being unreliable or uncommitted. I don't have any data on flexible work hours, but in 2011 a study found that only 4% of new fathers took over 2 weeks of parental leave. This is why it was so important when Zuckerberg took two months of parental leave -- it set an example and communicated to the company "men taking parental leave is normal".