Why is particle-wave duality a paradox?
I think because it seems to contradict itself proposing two opposite possibilities.
A paradox normally is a conclusion that goes against the common sense and that, starting from sound initial assumptions, seems to contraddict itself.
In this case I think it presents two possibilities apparently opposite and not compatible.
Light can be a wave AND a particle.
Starting from initial observations we can conlude that:
1) light is a wave (diffraction, interference...);
2) light is a particle (photoelectric effect).
Now we should choose (because we are used to have one answer only) and get only one conclusion but we cannot!