From what I understand, combining special relativity with quantum mechanics requires quantum field theory (QFT). Why fields?
I can see that for quantities already described by classical fields, such as the electromagnetic field, the quantum analogue will be some sort of field, but what is the motivation for describing particles in terms of excitations of underlying quantum fields?
A possible line of reasoning
Perhaps we wish to describe the creation and annihilation of particles, and perhaps this can be done through introducing creation and annihilation operators that act on the vacuum state. Such operators should act at each point in spacetime since particles can be created at each and every point in spacetime. Furthermore, such particles should be able to propagate continuously through spacetime and so the object that describes them should "operate" at each point in spacetime. Hence we should consider a field of operators, a so called quantum field?!