Why does Zermelo-Fraenkel set theory not allow a universal set?

Zermelo-Fraenkel (ZF) set theory does not allow a universal set primarily to avoid the logical inconsistencies known as Russell’s paradox.

In early, "naive" set theory, the unrestricted comprehension principle allowed for the formation of a set from any definable condition, including the set of all sets. However, this led to the construction of the set of all sets that are not members of themselves, which creates a contradiction: if the set is a member of itself, it must not be; if it is not, it must be.12

To resolve this "vicious circle," ZF restricts the comprehension principle so that it cannot form a set as large as the entire universe of all sets. Instead, sets are constructed through an iterative hierarchy where new sets are built from previously existing ones using operations like the power set. Consequently, any valid set in ZF must be smaller than the totality of all sets, effectively preventing the existence of a universal set within the system.13