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.
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The spin-statistics theorem associates integer-spin particles with bosonic exchange symmetry and half-integer-spin particles with fermionic exchange symmetry in relativistic quantum field theory under the standard locality and positivity assumptions.
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.