Punching up is a term for deploying powerful techniques of criticism and rhetoric to critique and dismantle power structures, rather than to harm people disempowered relative to yourself. It (apparently) comes from comedy, in which the idea is to make fun of powerful people and institutions rather than disempowered people.
Molly Ivins articulated the distinction in a 1991 People magazine interview:
"There are two kinds of humor. One kind that makes us chuckle about our foibles and our shared humanity -- like what Garrison Keillor does. The other kind holds people up to public contempt and ridicule -- that's what I do. Satire is traditionally the weapon of the powerless against the powerful. I only aim at the powerful. When satire is aimed at the powerless, it is not only cruel -- it's vulgar." 
As part of this, it may mean that if a conversation has an imbalance of power, the empowered party to it may be denied rhetorical tools available to the other, for example, the disempowered party might be snarkier without it being ethical for the empowered party to snark them right back.
Some examples might be:
- the ethics of flooding the Twitter mentions of a celebrity who said something sexist are different from those of flooding the mentions of someone from a disempowered group who said something snarky about your sexism
- the ethics of doxxing someone who is harassing you are different from those of doxxing a woman whose technical opinions you slightly dislike