Why is a horse placed under chordata?
Because the class Chordata includes all animals which are vertebrates !
Chordata is not something you "have." It is a way if classifying an animal. "Chordata" is a phylum in which vertebraes, urochodatas, and cephalochordates are put under (how they are classified). If your question was meant to be "are butterflies chordates" then the answer is no. Butterflies are classified under the phylum "Arthropoda," not under the phylum Chordata.