How did the unrestricted comprehension principle create problems in early set theory?

The unrestricted comprehension principle in early set theory assumed that for any given property, one could form a set containing all objects that satisfy that property. While this seemed intuitive, it proved to be fundamentally flawed because it allowed for the construction of paradoxical sets.12

The most famous issue arising from this principle is Russell’s paradox, identified by Bertrand Russell in 1901. Russell demonstrated that the principle allowed for the formation of the set of all sets that are not members of themselves: $\{x\mid x\notin x\}$. This leads to an impossible contradiction: if the set is a member of itself, it must not be a member of itself; if it is not a member of itself, it must be a member of itself.1

This "vicious circle" demonstrated that one cannot simultaneously assume a universal totality of all sets while allowing an unfettered principle to construct sets within that totality. Consequently, modern systems like Zermelo-Fraenkel set theory replaced unrestricted comprehension with more constrained axioms, such as the axiom of separation, to prevent such contradictions.12