Sherlock Holmes uses very cold, precise, rational language, shorn of all emotion. This is because he is a man of reason, a man with a piercing intellect who has no time for the kind of emotional connections that most people tend to seek out and cultivate in their lives. In his first exchange with Watson in the story, Holmes says, "I think, Watson, that you have put on seven and a half pounds since I saw you." This kind of cool, precise observation is representative of Holmes's speaking style.
It is all the more amazing, therefore, that Holmes should develop some kind of attachment to Irene Adler, whom he always refers to as “the woman.” To be sure, this isn't a romantic attachment, as Dr. Watson is at pains to point out. But it is an attachment, all the same, one based on a profound respect for Irene, arguably his most intelligent adversary yet.
Even so, Holmes maintains a calculated demeanor. His reference to Adler as “the woman” displays the same cold, rational detachment from life that characterizes his every other word. Whatever the true state of Holmes's feelings for Irene Adler may be, the language he uses remains the same as it was before he encountered her.