為什麼質子 中子 電子的自旋都是1/2呢?

Spin(自旋) can be construed as the [rotation] of a particle. Since a particle can be spinning cloclwise or anticlockwise, i.e. spinning [up] or [down], it has two different quantum states. Hence quantum numbers of 1/2 and -1/2 are assigned to the spins.
Electrons, protons and the like are classified as Fermions, which as a result of the Pauli exclusion principle, should have different spins in order that no two such particles can occupy the same quantum state.