Why is the Mass a Sacrifice?

Catholics talk about "The Holy Sacrifice of the Mass." But how was the Mass like those Biblical sacrifices of old - violent rituals with animals being cut up, set on fire and their blood being poured out on altars? The Mass I attended each week didn't look like that! But if we can understand Jesus' words at the Last Supper the way a first century Jew would, we'll come to see that Jesus didn't just give us his Body and Blood when he instituted the Eucharist. He gave us a way to encounter and enter into his sacrificial offering of himself on Calvary. Indeed, his sacrifice on the Cross is made present in every Mass. If we want to grow in sacrificial love, we want to participate more fully in the sacrifice of the Mass where we encounter sacrificial love Himself transforming our hard hearts a with his perfect love.