It is not that Sherlock Holmes cannot love. That is not the case at all. Quite the opposite.
Throughout his life, Sherlock was not sure of his ability, or apparent lack thereof. He had a certain amount of begrudging affection for his family, to be sure, but nothing that he could catagorize as something as inane as love.
Sherlock Holmes is capable of love. But much like the limited space in his brain for knowledge, he has a limited amount of space in his heart for love.
He did not know that the space was already filled by John Watson until he first laid eyes on the man that day in St. Bart's.
Sherlock Holmes saw John Watson and thought ah, so it's there after all.
For as small as he was, John Watson demanded quite a lot of space inside Sherlock's chest. All of it, in fact.
And really, he fit perfectly, as if the space had been carved out specifically with the doctor in mind.
And it had been.
It is not that Sherlock Holmes cannot love. It is that Sherlock Holmes's love has never been his own.
It has always belonged to John Watson.