My former company enacted a paternal leave policy around the time MSFT required suppliers/partners to offer them in order to continue doing business with MSFT.

Shortly after I became the manager of my team, one of my reports informed me that he wanted to use 3-4 weeks of paternal leave (out of a max of 6) a few months after the birth of his child (company policy allowed it within 12 months.) He said he'd keep his laptop nearby in case of emergencies. "You're crazy!" I told him, "take the full 6 weeks! And leave the laptop off!"

As a manager, if it's the company policy, then it's the employee's right to take the time off. There should be no amount of brow-beating (assuming sufficient advance notice, of course.) I checked in with HR for procedural details, and overall it was easy/painless from top to bottom.