"I’ve generally thought that it was adultery, or murder, or covering up sin, or all of the above. But looking again at the story Nathan tells, I this there’s more to it than this. ... I reckon that Nathan’s story sheds light on this. His story is about a wealthy man who has a lot of sheep who steals to one sheep his poor neighbour has in order to feed his traveler. The story is about greed and treading on others to get what you want. This was initially what got me thinking about the passage. Adultery and murder are strikingly absent from the story. ... I think this story is about the turn in David’s heart, to greed, to building his own empire and to pride. His methods (adultery, murder, lying, etc) are certainly deplorable, but the focus is on greed and his self-reliance."
However, I think David's greed and self-reliance are only secondary parts of David's adultery. Adultery is more then merely being naughty between the sheets, it is a complex knot of fidelity, possession and power. Sexual intimacy is a form of knowing and being known. I think that Nathan's story of taking of the other's man's lamb is symbolic of all that complexity.
The deeper sin is of course the continued disobedience against God that Adam originally introduced into the world. Pslam 51 says; "Against you, you only, have I sinned and done what is evil in your sight." Self-reliance and greed are only part David's adulterous act. We assume the murder, adultery and greed are tidy separate compartments of sin. An affair always involves more then sex, that's part of it's destructive power. So there's no need to mention all the facets of King David's sin, because it's summarized by Nathan's story and David's mea culpa in Psalm 51, which is of course the underlying sin of all our complex sins.
(If your married, Nicky Lock offers some useful advice that will hopefully go a long way in preventing this type of thing. (h/t Craig))
[Picture = David and Bathsheba, by Lucas Cranach, 1526.]