Opponents of positivism would point out that not everything in the world, especially in the social world, can be systematically categorised. There are aspects of society that cannot be understood and explained with numbers and figures. Sometimes there is a need for qualitative evidence.
This is especially relevant in social science because humans are neither controllable nor predictable. It is almost impossible to create controlled human environments and to do so would get in the way of finding the truth. This is because controlling the environment alters human behaviour, especially when they are being observed. This is known as the Hawthorne effect.
Moreover, controlling environments for experiments on society is highly unethical.