Chazal learn from the words: "והקטיר הכהן את הכל המזבחה" - “The Kohen shall make all of it smoke on the altar,” that even the horns and hooves of the animal are burned. Based on this, the Ohr Hachaim Hakadosh wonders: “If so, why did Avraham Avinu not offer his ram as a burnt-offering along with its horns (by the Akeidah)? Instead, he kept the horns as shofaros: the right horn for the shofar of Moshiach, and the left horn for the giving of the Torah.”

     R’ Shlomo Kluger zt"l (Imrei Shefer) explains that the Torah obligated offering up the horns of an animal only when it is the original sacrifice; where one donated a horned animal on account of a sin. However, if the korban is a substitute; for example, where someone first sanctified an animal which did not have horns, and afterwards substituted an animal which did have horns, in that case, he would not be obligated to burn the horns, since his original obligation was an animal without horns.

     Avraham Avinu only brought the ram as a substitute for his son, as it says, “and he offered it as a burnt offering, in place of his son.” Since Yitzchok did not have horns, Avraham was not obligated to offer up the horns of the ram. He was only obligated to offer up that which was comparable to his son, and no more.

     R’ Yitzchok Yaakov Weiss zt"l (Minchas Yitzchok) answers this question with a unique twist. He cites the words of the Kli Yakar, who explains why the law of the Korbonos requires that all parts of an animal be offered on the altar. We must offer up the horns because every sinner seems to possess “horns” with which to attack. Hence, as a penance, the horns of an animal must also be offered on the altar. Since Avraham’s ram was not offered for atonement, rather as a substitute for his son, it was not necessary for him to offer the horns of the ram. Instead, he found good usage for them: the Shofaros of Moshiach and Matan Torah.