"I'll burn the heart out of you," Moriarty had said.
And Sherlock had believed himself when he replied that he didn't have one.
But as John had once written, "Sherlock sees through everyone and everything in seconds. What's incredible though is how spectacularly ignorant he is about some things." Sherlock could solve a case in seconds with just a few glances around a room- he could read people's whole lives with the most seemingly insignificant of clues. But Sherlock was completely clueless when it came to the subject of human emotions… even his own were below his notice. Most of the time, Sherlock didn't even recognize their existence in himself.
In this capacity, Moriarty was Sherlock's superior. He had figured out the secret that Sherlock kept from himself. One look at John and Sherlock had told Moriarty what neither of them could admit. The way Sherlock looked at John, and John's fierce protectiveness over his friend, and Moriarty had deduced everything he had needed to know.
Sherlock had sincerely believed himself above those baser emotions when he had ridiculed Irene Adler for her "sentiment."
Yet, standing on the rooftop of St. Bart's, at the point of no return, looking down at the love of his life, he realized that Moriarty had been right. Sherlock had a heart, and it was breaking.