Do I take a tiny but not quite negligible emotional hit of feeling excluded every single time for doing that? what about people who program ada and type the name each day? Do you think most people even will notice that the 3 letter actually represent a name, a person, a woman, each time?
Some people would probably be more consciously aware than others of the fact that the 3 letters "bro" are a reference to "bro culture". Here are a few groups of people whom I think would be most likely to notice: People new to tech; women who've had bad experience with "brogrammer" types; "brogrammer" types themselves. It seems like a bad idea to adopt any policy likely to make the first two of those groups uncomfortable while signaling approval toward the third.
[0] Side notes: 1. Those professions are making a real effort to change these patterns to be more inclusive, too. And 2. Gender inequality in tech is nevertheless a more pressing problem than gender inequality in nursing, because tech is considered a higher status career.
Man, woman, brother... next command should be sister. Its a themed naming scheme.
But my point is that very few people will even think about a command they type in, especially if its just 3 letters. There are only so many 3 letter combinations, and even fewer that represent words.