Why was the art produced during the Dada movement considered art at all?

The art was in the hands of what the artist deemed to be art and did not have to meet a certain set of standards and rules.

Dada was an artistic and literary movement that began in Zürich, Switzerland. It arose as a reaction to World War I and the nationalism that many thought had led to the war. Influenced by other avant-garde movements - Cubism, Futurism, Constructivism, and Expressionism - its output was wildly diverse, ranging from performance art to poetry, photography, sculpture, painting, and collage. Dada's aesthetic, marked by its mockery of materialistic and nationalistic attitudes, proved a powerful influence on artists in many cities, including Berlin, Hanover, Paris, New York, and Cologne, all of which generated their own groups. The movement dissipated with the establishment of Surrealism, but the ideas it gave rise to have become the cornerstones of various categories of modern and contemporary art.