Actually, this is precisely the case. Please see: https://newdiscourses.com/2020/07/woke-wont-debate-you-heres-why/

The critical-thinking tradition is concerned primarily with epistemic adequacy. To be critical is to show good judgment in recognizing when arguments are faulty, assertions lack evidence, truth claims appeal to unreliable sources, or concepts are sloppily crafted and applied. For critical thinkers, the problem is that people fail to “examine the assumptions, commitments, and logic of daily life… the basic problem is irrational, illogical, and unexamined living.” In this tradition sloppy claims can be identified and fixed by learning to apply the tools of formal and informal logic correctly.

Critical pedagogy begins from a different set of assumptions rooted in the neo-Marxian literature on critical theory commonly associated with the Frankfurt School. Here, the critical learner is someone who is empowered and motivated to seek justice and emancipation. Critical pedagogy regards the claims that students make in response to social-justice issues not as propositions to be assessed for their truth value, but as expressions of power that function to re-inscribe and perpetuate social inequalities. Its mission is to teach students ways of identifying and mapping how power shapes our understandings of the world. This is the first step toward resisting and transforming social injustices. By interrogating the politics of knowledge-production, this tradition also calls into question the uses of the accepted critical-thinking toolkit to determine epistemic adequacy. To extend Audre Lorde’s classic metaphor, the tools of the critical-thinking tradition (for example, validity, soundness, conceptual clarity) cannot dismantle the master’s house: they can temporarily beat the master at his own game, but they can never bring about any enduring structural change. They fail because the critical thinker’s toolkit is commonly invoked in particular settings, at particular times to reassert power: those adept with the tools often use them to restore an order that assures their comfort. They can be habitually invoked to defend our epistemic home terrains. (pp. 881–882)

Here, the “master’s tools” are explicitly named by Bailey as including soundness and validity of argument, conceptual clarity, and epistemic adequacy (i.e., knowing what you’re talking about) and can easily be extended to science, reason, and rationality, and thus also to conversation and debate. The “master’s house” is the “organizational schemata” laid out by Kristie Dotson as the prevailing knowing system. Her claim is that these tools—essentially all of the liberal ones—cannot dismantle liberal societies from within, which is their goal, because they are the very tools that build and keep building it.

Bailey’s point is clear: the usual tools by which we identify provisional truths and settle scholarly disagreements are part of the hegemonically dominant system that, by definition, cannot be sufficiently radical to create real revolutionary change (a “third-order” change, as Dotson has it). That is, they can’t reorder society in the radical way they deem necessary. The belief, as both scholars explain in different ways, is that to play by the existing rules (like conversation and debate as a means to better understand society and advance truth) is to automatically be co-opted by those rules and to support their legitimacy, beside one deeper problem that’s even more significant.

The deeper, more significant aspect of this problem is that by participating in something like conversation or debate about scholarly, ethical, or other disagreements, not only do the radical Critical Social Justice scholars have to tacitly endorse the existing system, they also have to be willing to agree to participate in a system in which they truly believe they cannot win. This isn’t the same as saying they know they’d lose the debate because they know their methods are weak. It’s saying that they believe their tools are extremely good but not welcome in the currently dominant system, which is a different belief based on different assumptions. Again, their game is not our game, and they don’t want to play our game at all; they want to disrupt and dismantle it.