Hayek is a puzzle. Certainly he started out as one for me, now some twenty-odd years ago. - Bruce Caldwell

He linked the notion of a spontaneous order that forms when agents follow (often simple) rules with the idea of complex systems in the 1950s. This was a critical breakthrough, for it allowed him to drop the old natural science-social science dichotomy ...

It seems evident from his unpublished piece that his reading of the Mill-Taylor letters gave Hayek a bit of a shock. He knew, of course, from the Autobiography that Mill had an elevated opinion of Mrs. Taylor. The letters seem to have convinced Hayek that she dominated him. Hayek would doubtless have seen this as a weakness, and he might well have lost some respect for Mill as a result. It may also have provided a convenient explanation for Hayek for why a great mind like Mill might nonetheless “desert” the liberal camp. (Hayek’s hope to lead others to the same conclusion might have helped motivate him to write the book on the correspondence between Mill and Taylor.) Given what has sometimes been said about the dominating personality of Hayek’s second wife, one wonders whether Hayek would later in his life have felt even more commonalities with Mill.

It is probably best to start off by noting that Hayek knew a lot about Mill, probably for a time more than any other contemporary scholar. So we should not underestimate him.
Next, what he had to say about Mill, what portion of Mill’s work he drew upon, was very much dictated by the sort of project he was working on. When he was making an argument about how the British liberal tradition lost its bearings, or about how Comtean positivism came to be known and gained influence across Europe, Mill was classed among the perpetrators. When he was writing about what made the British liberal tradition great, Mill could be one of the heroes. There is, I think, no inconsistency in the fact that Hayek could hold both views simultaneously.