The writing style that shows the irrationality of human existence is called absurdist.
Absurdist fiction refers to a genre of fictional narrative most often in the form of a novel, play, poem, or film, that deals with the experiences of characters in situations where they cannot find any purpose in life. This is illustrated by meaningless actions. Some elements in absurdist fiction include satire, dark humor, incongruity, the abasement of reason, and controversy