Why do Muslims sacrifice livestock (goat, sheep, cow etc.) on Eid Al-Adha?
The animal sacrifice is to honor the willingness of Abraham to sacrifice Ishmael, his eldest son, as an act of submission to God's command. At the point of sacrifice, God intervened and replaced his son with a ram (male sheep) which had been slaughtered instead.
Abraham had passed the test by his willingness to carry out God's command