Video "The Biggest Ideas in the Universe | 17. Matter by Sean Carroll (2020)" at youtu.be/dQWn9NzvX4s?t=3707 says that no one has ever been able to come up with an intuitive reason for the proof.
Articles by others on the same topic
The Spin-Statistics Theorem is a fundamental principle in quantum field theory that governs the relationship between the intrinsic spin of particles and the type of statistics they obey. It provides a foundational explanation for why particles with integer spins (such as photons and W/Z bosons) are described by Bose-Einstein statistics, while particles with half-integer spins (such as electrons and quarks) are described by Fermi-Dirac statistics.