In many stories of great civilizations, one of the elements that brings them to their downfall is a treacherous member of society that inevitably betrays the society and brings it to its downfall.
People often bring up questions like, "If the Ancient Kingdom was so powerful, how did they fall?" I think one of the most likely explanations is that someone important in the old Ancient Kingdom acted as a Judas of sorts - betraying the kingdom and leading to its downfall.
Taking that a few steps forward and going along with the theory that the D's are in fact quasi-reincarnations of people who lived in the Ancient Kingdom, there's undoubtedly one person who fits the potential description of a Judas-character perfectly - Blackbeard.
Of all the D's in the story, Blackbeard is the one that is the most dissimilar to the others. Yet, the easy explanation of, "Oh he's a fake D." seems to be a copout that isn't putting much thought into it. Blackbeard is treacherous and power hungry, and would seemingly betray anyone or anything to achieve his goals. His first betrayal in the story was the WB pirates. His second betrayal was the World Government. It's not a big stretch to think that whomever Blackbeard was in the Ancient Kingdom may have been the catalyst to its downfall by betraying the Kingdom to the alliance of nations that would become the World Government.
The story really only allows for the above to be speculated on firm ground. For the last part of this post I'll throw out a few potential meanings for the above for later in the story.
One of the potential implications of the above, is that whatever One Piece is now, is what Blackbeard wanted back in the Ancient Kingdom days. Something he wanted to the degree that he'd betray his entire country to obtain it. On that same note, it also seems to indicate that Roger/Luffy was some sort of protector of that artifact, and its rightful heir. This certainly seems to throw One Piece into the category of an artifact that holds a high degree of power - or at least something that can corrupt those who aren't pure of heart like Luffy.
Another implication for this theory, is that it more definitively sets up Blackbeard as the "final" opponent in the story - something which continually gets emphasized more and more ad the story goes along. It wouldn't surprise me if such a final battle ended with some sort of event that breaks the D. cycle of reincarnation entirely.
And finally on a last note - going into 1000% speculation territory here that's far less likely to be true than anything above. What if One Piece, as an Ancient Kingdom treasure, is actually the artifact responsible for the continual reincarnation of those who are D's? If One Piece had such a use, it might explain the reasoning behind why Blackbeard betrayed the Ancient Kingdom in the first place - to use One Piece and achieve a sort of immortality for doing so.
**TLDR-
Main Point:
Blackbeard was a traitorous member of the Ancient Kingdom that caused its downfall. Thus his difference from other Ds.
Speculation Points:
Blackbeard may have betrayed the Ancient Kingdom to gain what we now know as One Piece.
Luffy may have been the protector of One Piece back in the Ancient Kingdom days.
One Piece as an artifact might be the source of the Ds reincarnation.
Blackbeard's betrayal might have been to use One Piece and put himself in the reincarnation cycle even though he was unworthy.**