They deny the existence of the soul, because acknowledging the existence of the soul implies a place in which the soul must reside after death (conservation of energy), and thus acknowledges an afterlife and a God (and a devil, and sin, and any other subject pertaining to the divine).
“…Judge not what a man has done, but judge what he could have done if he was a different bloke altogether. For art thou a leper? And a leper can changeth his spots…” --Rudy Wade, Misfits (Series 4, Episode 8)