High School Relation between spin and symmetry of wave function

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The relationship between spin and symmetry in wave functions is rooted in the spin-statistics theorem, which states that bosons possess symmetric wave functions and have integral spins, while fermions have antisymmetric wave functions and half-integral spins. This distinction arises from the fundamental principles of quantum mechanics and the behavior of particles under exchange. The theorem is not merely empirical; it is a theoretical deduction derived from the underlying mathematical framework of quantum field theory. Understanding this relationship is crucial for explaining the statistical behavior of particles in various physical systems. The spin-statistics connection is a foundational aspect of particle physics.
Jigyasa
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Why is it that bosons (particles having symmetric wave functions) have integral spins and fermions (particles having antisymmetric wave functions) have half integral spins? A lot of books state this without specifying the reason. I was wondering if this is a theoretical deduction. Or is it an empirical fact. Any help would be great!
 
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