Why did Frege’s revised axiom fail to solve the contradiction in his system?

Gottlob Frege’s attempt to resolve the contradiction identified by Bertrand Russell—known as Russell’s paradox—involved modifying one of his axioms in an appendix to the second volume of his Grundgesetze der Arithmetik.

This revision failed to solve the underlying inconsistency in his system because, as was later demonstrated by the Polish logician Stanisław Leśniewski, the modified axiom still led to a contradiction. Furthermore, while Frege may not have discovered this specific failure, he would have realized that the change rendered several crucial proofs from the first volume of his work invalid, as they could no longer be successfully derived within the modified system.1