Criticism as a discipline and an approach to analyzing (and therefore appreciating) works of art has a long history in Western culture. Traditional literary criticism before the Chicago School of the mid-20th century involved establishing writer A's influence over writer B (Trollope's influence on Dickens, for example). There is also the critical question of "appropriateness" by which, in traditional criticism, is meant ethically or morally appropriate--a piece of literature that advocated inequality, for example, would be "criticized" by the Greeks.
Finally, traditional criticism was free from outside, or "hidden" agendas or slants. One of the major contributions of deconstructive criticism is how it reveals hidden biases in the author.