Momentum must be conserved, however this is not the explanation for the neutrino.

Neutrinos are part of the weak interaction. You correctly expect a positron on the right side of your reaction because of conservation of electric charge.. But why? Well conservation of electric charge is a consequence of the law of the force of electomagnetism. In radioactive decays the 'Weak' interaction comes into play and is in some ways similar to the electromagnetic force (and different in some ways and slightly more complicated). But it is similar in the way that there are also charges that must be conserved in the Weak interaction. In particular there is something called lepton number for each flavour of lepton which are the electron, muon and tauon. And this lepton number must be conserved.

But this comment on the neutrino and momentum conservation is indeed important, and it is an obvious question - why do we 'need' the neutrino. Historically we saw several types of radioactive decay and some of them (alpha and gamma) always had a fixed energy of the emitted particle e.g. gamma decay of an excited nucleus A*->A+gamma. Energy and momentum conservation of such a process where 1 particle turns into 2 predicts that the emitted particle will always have the same energy in every decay.

However for beta decays where an electron is emitted it was observed that the electron energy was a spectrum up to some upper energy - contradicting the 1 to 2 particle decay and therefore physicists postulated the existence of an additional very light particle being emitted in this decay such that the energy was split between the electron and the postulated 'neutrino' as this could explain the spectrum seen. This was how the neutrino was first discovered.