You need to know two facts: 1) A massless object will travel at the speed of light. A massive object, on the other hand, as long as it may accelerate, will alw

You need to know two facts: 1) A massless object will travel at the speed of light. A massive object, on the other hand, as long as it may accelerate, will always travel at smaller speeds. 2) When you are travelling at the speed of light you don't experience time, it is completely frozen. If you could ride a photon time would freeze. This is the notion of proper time, in physicists' terms. Think of the twins paradox, it's similar, albeit not identical... So if a neutrino were massless, as predicted by the Standard Model, it wouldn't experience time and it wouldn't oscillate. Oscillating requires time. It follows that, as oscillations are observed, the neutrino must experience time, and have a mass. This mass is quite tiny, we don't know its value, we just know upper bounds.