Deconstruction?

Lately I have been engaged in the study of semiotics, specifically structuralism and deconstruction, for my art criticism class.  After multiple readings of various sources I am confident that I mostly understand structuralism, especially after stumbling upon this explanation by Daniel Chandler, if you are interested. http://www.aber.ac.uk/media/Documents/S4B/sem02.html    However, I am having a difficult time wrapping my head around deconstruction, especially when asked to write a deconstructionist analysis of a piece of artwork considering that deconstruction is not actually an analysis or a critique but more like a taking apart of another analysis.  So, I was thinking about my own work and how this critique and non-critique would work with a piece from my latest work.   Using the work I posted previously, depicting myself in a struggle against myself, I would say that the structuralist reading of the image is very straightforward.  The two selves symbolize an internal struggle which results in a killing of one part of the self, with the pillows being a signifier for the concept of suffocation and thus a sign or symbol of repression.  Thus a metaphor for the self being the only thing that stands in the way of ones successes is created.  So, the structuralist approach to reading a work of art is essentially just a way of putting meaning into a structure.  I think that this is a facet of human nature that is instinctual; we all want to put everything in an order or a category so as to make sense of the world.  However, when I attempt to take this same work and make a deconstructionalist reading of the work, I find myself questioning the purpose of deconstruction.  Deconstruction works by finding binary oppositions, placing importance on one and then reversing the meaning.  So, if the primary binary opposition is suffocation or repression vs. surviving or expression and emphasis is placed more on suffocation or repression when reversed the work is read to be about surviving or expression.  So then I suppose a deconstructionalist would read the work as two selves not in a struggle but in an agreement with the self that is lying down being in acceptance of the situation in order for the other to live?  After my own struggle with the deconstruction reading the only thing I can be sure of is that there are multiple interpretations to any work of art and that interpretations are not really right or wrong.  In any case I don’t really think it matters in the end, expect when I write my thesis.