For the execution of massive volumes of waste waters rich in organic matter, why is aerobic degradation more important than anaerobic degradation?

It is because facultative and aerobic microbes that occur naturally such as protozoa, fungi, bacteria etc residing in the wastewater can rapidly oxidize soluble organic and nitrogenous compounds. The process if further accelerated due to mechanical addition of oxygen hence eliminating most of the pathogenic content of the effluent.