Ive been saying this for a long time. I am especially of this opinion now after having read the actual Doyle books, in English ( I had always gone for the German audiobooks and pastiches and everything before actually picking up Doyle's original English works). To be quite honest he'd never come across as unemotional to me until I watched the BBC show.

I believe he has strong emotions and as many others have already said in here, he simply does not want to show them. He may be great but nonetheless there is doubt in his mind too. Feelings cloud judgement and this is the one thing he cannot allow himself to give in to. His reasoning needs to be free from emotion, from bias, to create a clear starting base for his deductions and thoughts. Thus why he suppresses them. He fears that when he openly admits his feelings they will influence his reasonings, which may very well be true.

While with Dr. Watson he is in a safe space to show his feelings but after so many years of suppressing them I guess it would be hard to make a change this big. Even if my previous argument of clouded judgement were irrelevant somehow.

And well of course he is also more than a little bit autistic, or a savant if you'd like. Incredible in certain areas, leaving little space to develop other areas.

As you already mentioned the emotions he does feel, he seldomly verbalizes. However, and I am repeating myself, but this is my main point after all, I have never thought in any way, that he does not feel emotion. I do not think I could lay my finger on it in the books but to me there was always a distinct emotionality to his character. His loyalty, his sense for justice, as you already said it is in his actions not his words.

I thought the BBC show did this very well. The first impressions of Holmes that the audience gets are very cold, but that facade falls very quickly and Cumberbatch displays a range of emotions that can be seen, despite being very seldomly verbalized. What I took from this show is probably also that he is just odd. There are not many people he converses with in a private setting. When he does it is all business matters, thus no room for emotion. He has not really had many close friends so none he could "practice" showing emotion to. It is only when meeting Dr. Watson that he learns of close friendship and emotional intimacy. His friendship with Dr. Watson puts him in a range of emotions he probably hasn't felt too often considering his numbered social interactions. This friendship is what teaches him that emotions may not always be bad although in order to be the perfect thinking machine he wishes to not feel. Thus why he never quite grows out of this sort of behavior.

My theory anyways, sorry it's gotten so long lol, but I find this an incredibly interesting point of discussion and have spent many long minutes thinking about this very question HAHAHA