Step 1: Conservation Laws:
In beta decay (specifically $\beta^-$ decay), a neutron turns into a proton and an electron (beta particle).
To conserve spin and lepton number, another particle is emitted.
$n \to p + e^- + \bar{\nu}_e$
The electron has lepton number +1. To keep total lepton number zero (as for neutron), the emitted particle must have lepton number -1. This is the antineutrino ($\bar{\nu}_e$).