The secret is depression.

Okay, I feel a need to help explain this movie from my point of view. First, we must consider the source, the writer/director "Lars", suffers from extreme depression, to the point he was hospitalized for two months before AntiChrist was filmed, during this time his depression played a HUGE part in the writing, filming and theme of the film. This film is also the first in a series of three films which Lars calls "The Depression Trilogy". The second film is called Melancholia, the third yet unfilmed movie will be called Nymphomania. ALL THREE FILMS ARE A REPRESENTATION OF HOW THE MIND PERCEIVES DEPRESSION!

In this sense, keeping in mind that Lars originally wanted this to be seen as A HORROR FILM about depression, but he admitted to missing the mark in his goal, we can infer that everything that happened in AntiChrist happened because the two grieving parents were trying to make sense of their grief and depression over the loss of their child. Kind of like if you watch a movie about ghosts and suddenly you are afraid to walk down a dark hallway alone, you know in your mind that their are no ghosts but you still try to make sense of your emotions in irrational ways, like turning on a light will chase the ghosts away.
So to sum it up, this movie is entirely about the actions of two educated people who try to find meaning in their grief by assigning meaning where their is none. The woman starts to blame herself and sex for her depression and maddness leads her to torture her husband and herself. He focuses solely on her depression, while trying to ignore his own and eventually he also spirals into her madness.

If you search for anything deeper than that then you to are searching for answers that aren't there.