I'm fighting against speech that dehumanizes Jews, LGBT, Blacks, and so on; and ensuring that people who engage in it face consequences for that speech. This gets back to Hannah Arendt's paradox of tolerance.
At what point am I allowed to fight back? If someone advocates exterminating me, do I have your permission to suggest that their speech should have consequences? Or do I have to wait until I'm dead?
Do you believe that most people getting "mob cancelled" right now are overtly advocating extermination? If so, can you provide a few examples so I can better understand your position?
The conclusion his argument leads to is: In a tolerant society, attacking people because of their beliefs is not permitted (requisite intolerance).
You don't fight against speech, you speak against its ideas.