How did Bertrand Russell’s barber paradox reveal a problem in Frege’s system?

Bertrand Russell’s discovery of Russell’s paradox revealed a fundamental inconsistency in Gottlob Frege’s logical system by exposing the dangers of his unrestricted comprehension principle.12

Frege’s system allowed for the formation of a set based on any condition, asserting that for every formula, there exists a set containing all elements that satisfy it. Russell demonstrated that this principle permitted the construction of the set of all sets that are not members of themselves—a set that leads to a contradiction: if it is a member of itself, it cannot be; if it is not, it must be.213

Russell illustrated this logical flaw using the barber paradox: a barber who shaves all those, and only those, who do not shave themselves. The question of whether the barber shaves himself creates an impossible situation where any answer contradicts the premise. This revelation deeply impacted Frege, who recognized that it threatened the logical foundations of arithmetic, ultimately leading to the development of type theory and other axiomatic restrictions to avoid such "vicious circles".231