The bottomline is: light is
neither a
wave nor is it a
particle! It is in fact something entirely else. It just happens that the behaviour of that "something", in certain cases, can be adequately described with the mathematical
model of a wave, and in some other cases, it behaves more like a particle.
Quantum mechanics are a, more or less successful, attempt to create a single, non-contradicting model that explains both kinds of behaviour.
Too often, people for get that physics doesn't deal with reality, only with mathematical models of some of its aspects.