The main points of contention between Mill and Comte from the start were a methodological issue and a social one.
The method of inquiry centered on the foundation of social science. Comte argued that physiology was the foundation for sociology and accorded phrenology complete scientific standing. Mill was hesitant to abandon psychology, which he saw as the proper foundation for social science, in favor of untested physiology.
When Mill questioned women’s position in the ideal society, this social problem was brought up. The questionable physiological justifications Comte used to support the denial of equal intellectual standing to women were unacceptable in Mill’s eyes because of his sensitivity to the social position of women. Nevertheless, mills maintained the notion of equality between men and women.
Comte could not provide adequate evidence of the alleged link between the theological school of thought and the military social structure. Moreover, according to Mills, Comte lacked sufficient understanding of English social and political institutions.
Due to this transition from positivism to creating a religion of humanity, Comte lost many followers and intellectual acquaintances, including J.S. Mill of England.