If you are fully satisfied with classical logic and set theory as foundation of mathematics, no chance to convince you in a few words that univalent foundations can be "better". If you are not fully satisfied, you should take time to understand the concepts behind univalent foundations to see if it solves your frustrations.

Mathematicians interested in foundation of mathematics should take time to understand how logic and structures are handled in HoTT (Constructivity, propositions as types, proofs as programs, equality as identity types), and why this can be seen as a generalization of classical logic and standard set theoric constructions.

A theory that generalizes classical logic and set theoric constructions is likely to be a better foundations for mathematics, at least from the "philosophical" point of view, if not from a practical one.