> That’s why we have worked hard to cultivate a “no apologies” leadership style in our workplace.

So ... Instead of, "Sorry, I got to leave the meeting to catch the Go Train" at which point the woman (man) leaves in the middle of the meeting. 

it's, "I'm leaving the meeting to catch the Go Train" at which point the woman (man) leaves in the middle of the meeting. 

Sounds like a recipe for rudeness.