I'm assuming that this was a double-entendre pun on "man" (short for manual) also meaning "human of male sex", and using a word related to the second meaning to give "bro".
It's similar to the situation of how "rake", derived from "ruby-make" gave rise to "hoe", riffing off the meaning of "rake" as a garden tool.
It's not clear to me how a woman using the "bro" tool at her computer would somehow be marginalized or excluded. Puns aren't automatically sexist just because they reference some aspect of maleness/femaleness.