The first major divergence from the traditional bullfight is that Picasso de-emphasizes the traditional and human aspects of the bullfight attributed to the matador and embodies those and more in the horse to make it a symbol of domestication and humanness. La Corrida (1900), one of those first pastels, shows a group of matadors entering the field to fight and kill the bull. They all have their backs to the viewer and the perspective of the painting puts the colorful matadors in sharp juxtaposition with the dark bull. One can already see the beginnings of the decline and stripping of the matador of symbolic significance as even in these first paintings the matadors have no personality or weight; rather they have physically turned their back to the viewer. The beginnings of Picasso’s “disinterest” in the matador in the bullfight themed art can be seen by the pastel La Corrida, where the bull is literally in the limelight, and the matador is in the darkness. As a testament to this trend, in the later piece Bullfight: Death of the Torero (1933), the picador is just a casualty of the clash between the horse and the bull. 
The atavistic crowd is nonexistent as all the humanity is found within the gracefulness of the horse’s arched neck. He is the sole representative of this picador/horse/crowd team. Why the de-emphasis of the human aspect of the bullfight? The matador represents the tradition, institution, and glorification of man over beast, and Picasso chooses to reduce this feature of the bullfight in favor of the tragic horse and a strange but rhetorical sort of congruency and consistency of an animal vs. animal conflict.
Images
Above:Picasso, Pablo. “La Corrida.” 1900. Private Collection.
Below:Picasso, Pablo. “Bullfight: Death of the Torero.” 1933. A Picasso Bestiary. London: Academy Editions, 1995.