Why do all fermions have the same spin 1/2?

Shen712 said:

TL;DR Summary: Why do all fermions have the same spin angular momentum ##\frac{\hbar}{2}##, regardless of their different masses?

We are taught that all fermions have spin ##\frac{1}{2}##, short for spin angular momentum ##\frac{\hbar}{2}##, which can be added to the orbital angular momentum. Considering spin is a kind of angular momentum, it must be dependent on the mass (or moment of inertia) of the particle. However, different fermions, such as proton, neutron, quarks, neutrinos, and electron, have different masses. But why do they have the same spin angular momentum ##\frac{\hbar}{2}##?

PeroK said:

The quantisation of angular momentum is a stunning achievement of mathematical physics. Angular momentum cannot take any value, but but only multiples of ##\frac \hbar 2##.

Orodruin said:

OP’s question was why all fermions have spin 1/2 though. They don’t.