“Political correctness” and “cancel culture” are two concepts frequently invoked to control speech and influence debates with a view to establishing greater equality across the globe. Even though their usage has also been met with criticism, there is a strong merit in these attempts, as language change is indicative of wider cognitive changes that are eventually also transformed into changes in the law and society. Based on the wider trend of a rise in so-called “essentially oxymoronic concepts” in public discourses in general and equality debates in particular, this article proposes to analyse the present linguistic trends in order to better understand the deeper causes and related challenges to legal reasoning posed by “political correctness”, “cancel culture” and other terms that have been qualified as oxymora or paradoxes. Based on the view that oxymora and paradoxes are not mere aspects of language but also expressions of deeper layers of human cognition, the article ponders the need not merely to control the external aspects of language use but also to inquire more deeply into the inner workings of the brain and its underlying cognitive processes. In this endeavour it critically examines the dominant modes of dualistic or dichotomized thinking and binary logic, which – when regarded in isolation – appear to cause most discriminatory acts and violations of the principle of equality.