When the isotope Nitrogen-14 (which has a nuclear spin of 1) undergoes beta decay, it releases an electron, which has a spin of -1/2. Since the mass of the Nitrogen-14 isotope stays the same (albeit, it changes by a negligibly small amount), the angular momentum would stay the same. This violates the conservation of angular momentum as the sum of the angular momenta, is 1/2 (which is smaller than one). Therefore the anti-nuetrino released must have a spin of 1/2? Is this explanation correct, and if not, why? Are their any other explanations of the 1/2 spin of antinuetrinos? And if there is, what are they?
Spins are angular momenta. Angular momentum is a vector, and conservation of angular momentum imposes the sign on the spin found. If in a reaction the electron goes off with a spin -1/2, the antineutrino-electron ( which conserves lepton number) has to have +1/2.
The title though
Why do antinutrinos have a spin of 1/2?
is not concerned with the vector sign, but with the assignment of spin 1/2 . That spin 1/2 was necessarily assigned, and fermions were discovered, is also due to angular momentum conservation. If this assignment were not given to electrons and protons and neutrons back when they were new discoveries, physics would have to give up on angular momentum conservation, which is still one of the main (axiomatic) laws in physics theories, classical and quantum mechanical.
Conservation of energy and momentum in decays forced the neutrinos existence , and conservation of angular momentum assigned their spin. At first, experiments assigned a zero mass to neutrinos, but the existence of neutrino oscillations shows that a small mass has to be assigned to them, although experimentally there are only limits.
Conservation of lepton number shows that antineutrinos have to be there. and this is included in the standard model, of particle physics . At present the standard model has not been falsified, and it is very good at predicting new phenomena.