Why does the concentration-mass relation of galaxy clusters have a negative slope?
The hierarchical picture of cosmology posits that the smallest structures formed first, early in the evolution of the Universe, and that more massive systems assemble from these initial structures.  The smallest structures therefore have the highest concentrations according to the picture you present, as the Universe had a higher mean density at the time. As the Universe evolves, the average density decreases, and the largest systems form from the smaller structures. Therefore, the higher the mass of the system, the smaller the concentration, whereas the smallest structures keep their initial concentration from their formation time.

The key here is that smaller structures are older than larger structures, therefore have a higher concentration.