Why can a set of all sets lead to contradictions under unrestricted comprehension?

The assumption that an unrestricted comprehension principle allows for the formation of a set of all sets—or any set defined by an arbitrary condition—leads to logical contradictions because it permits the construction of self-referential, paradoxical sets.12

The most famous example is Russell’s paradox, which considers the set $R$ of all sets that are not members of themselves: $R=\{x\mid x\notin x\}$. This definition creates an impossible situation:13
* If $R$ is a member of itself ($R\in R$), it must satisfy the condition of not being a member of itself ($R\notin R$).12
* If $R$ is not a member of itself ($R\notin R$), it fulfills the condition for membership in $R$, meaning it must be a member of itself ($R\in R$).12

Because both scenarios lead to a contradiction, the unrestricted principle is considered flawed. To resolve this, modern set theories, such as Zermelo-Fraenkel, restrict comprehension to prevent the construction of sets that are as large as the "universe" of all sets, effectively prohibiting the existence of a universal set.12