I conjecture that Holmes—surprisingly given his distinguished lineage, his professional success, his commanding presence, and his wartime prowess—did not take himself very seriously. He was a wit, and wit implies a sense of incongruity, including the incongruity between one’s pretensions and one’s achievements. If you do not take yourself very seriously you are unlikely to fool yourself into thinking you have all the answers.
I don’t know how strong the basis for that conjecture is – I don’t recall having seen the point made before – but I like it. Seems like the sort of thing there ought to be more of.