Punching up is a term use when someone engages in a
conflict with an
adversary who has greater power/status then themselves. It's also known by the phrase: "Speaking truth to power". The antonym of "Punching up" would be "Punch down", wherein someone engages in a conflict with an adversary who has less power/status then themselves.
Person 1: What does it mean to "
punch up"?
Person 2: Well, say that you engage a Feminist in a debate. You would be
punching up since Feminism is the status
quo (Meaning it has societal power/status.) and debating it in any form would mean having to challenge someone with more power than you yourself has. You're "punching up" at the person who is above you.