The Return of Sherlock Holmes
How we cite our quotes:
"You can't help it, my dear Watson. You must play your cards as best you can when such a stake is on the table. However, I rejoice to say that I have a hated rival, who will certainly cut me out the instant that my back is turned." (Milverton.1.61)
It is practically a point of pride for Holmes to have a "hated rival." He's definitely a little bummed after Moriarty is gone and Holmes, like any good superhero, seems to think that he needs a nemesis around to make life interesting.
"Perhaps when a man has special knowledge and special powers like my own, it rather encourages him to seek a complex explanation when a simpler one is at hand." (Abbey Grange.70)
The fact that Holmes describes himself, even as a joke, as having "special powers" really demonstrates his pride and arrogance. The man has healthy self-esteem at least.
"I am fairly familiar with all forms of secret writings, and am myself the author of a trifling monograph upon the subject, in which I analyze one hundred and sixty separate ciphers, but I confess that his is entirely new to me." (Dancing Men.154)
Holmes has trouble doing humble. He's clearly trying to downplay his success and brilliance here, or perhaps emphasize it by using false modesty. At any rate, Holmes is so super awesome that he can't come off as modest even if tries. Which he usually doesn't.