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Sides in the debate are talking past each other
There's no common ground on public discourse about Cancel Culture because sides are taking stances which are orthogonal, not opposing. One side requires a rational debate based on a classic understanding of freedom of speech; the other side denounces how people with a favoured position can impose their point of view without allowing any viable opposition.
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A classical understanding of freedom of speech requires that all ideas can be expressed, maintaining a neutral tone and exploring them rationally to their ultimate consequences; otherwise, it is impossible to perform an adequate problem-solving of the social issues through insightful compromise ideas that satisfy all sides. This kind of debate has been done in controlled discussion environments, within members of the same social class, or at least among representatives of groups with comparable strengths.
The social networks on which today's public discourse is largely maintained bear no resemblance to the parliaments of the past. These media concentrate the force of the protest on a few prominent figures, who get burned by the strength of harassment, and the debate becomes polarized towards the extremes. Signatories claim that this dynamic prevents controversial ideas to be expressed, impeding adequate analysis of the problem due to the Internet shaming, and threatening the people who tried to explore them. This is similar to the worst of McCarthyism, witch hunts or public lynchings. Opponents claim that voicing disagreement with those who express such controversial ideas is also part of free speech. Also, that there's an inherent imbalance between the reach of public people who can get their message across to their huge number of followers, and critics who individually have only a few listeners and whose position has little impact.
Open debate requires both the free exchange of ideas an speakers on a similar level of power The Signatories denounce the lack of a free exchange of ideas The Antis denounce the lack of speakers on a similar level of power