Sometimes it is hard to explain to people why the sacrificial nature of Christ's death is relevant to the question of the scope of the atonement: i.e. whether the atonement was made for all, hypothetically all, or particularly the elect. One way to explain this is by reference to the fact that Christ is not just the lamb of God, whose death takes away the sins of the world, but that Christ is also the High Priest who makes the offering. The following provides an easy explanation of this argument, so that you can present it to your friends, without requiring them to know everything about the Old Testament sacrificial system.
At the heart of it, the offering of a lamb as a burnt offering involved killing the lamb and roasting it in fire. That's quite similar, as hopefully you've noticed, to the core of having lamb for dinner. What then differentiates lamb chops from a sacrifice?
It's not the fact that the lamb can still be eaten in the dinner context. Yes, there were "whole burnt offerings" where the entire animal was fully consumed by the fire, but the more typical context of animal sacrifices involved the cooked animal being eaten - partly by the priest and partly by the person offering the sacrifice. That's why the apostles taught gentile Christians, you may recall, to buy their meat without asking whether it was a sacrifice to one of the gods. So, it is not the degree of cooking that distinguishes the sacrifice from the dinner.
Instead, what distinguishes the two is the ritual, especially the prayer. The prayer asks God to accept the animal as a sacrifice and consequently to accept the person for whom the sacrifice is offered.
Furthermore, sacrifice could be made for one person or a group of people. For example, when sacrifices were made on behalf of Israel as a nation, sometimes lots of animals were killed, but there was not a one-to-one relationship between the animals and the people of Israel. Likewise, in some cases a sacrifice might involve more than one animal, but only one person. How could these situations be distinguished?
Again, the answer lies in the ritual - particularly in the prayer. The prayer is what distinguishes a sacrifice from one person from a sacrifice for a family, tribe, or nation.
Now, apply that principle to Christ's death. For whom does Christ pray? Does Christ pray for all mankind indiscriminately? Or does Christ pray for all the believers - all the elect? Does Christ specifically pray for those given to him by the Father?
In theological terms, this is the "impetration" aspect of the atonement - for whom does Jesus ask the Father for forgiveness of sins and eternal life? Without any request, the sacrifice is just a tasty meal. With the request, the sacrifice is made for the people identified in the request.
Now, someone might try to claim that Jesus asks for life for everyone, but the Father turns Jesus down except in the case of those who make the difference and autonomously cooperate in some way. Such an idea, though, lacks any Scriptural testimony and drives a wedge between the Father and the Son, which contradicts the idea that "I and my Father are one."
Indeed, the Scriptures do not describe that Jesus prays for each and every individual, that the Father would accept His sacrifice on their behalf. For example, Jesus says: "Father, the hour is come; glorify thy Son, that thy Son also may glorify thee: as thou hast given him power over all flesh, that he should give eternal life to as many as thou hast given him. ... For I have given unto them the words which thou gavest me; and they have received them, and have known surely that I came out from thee, and they have believed that thou didst send me. I pray for them: I pray not for the world, but for them which thou hast given me; for they are thine. And all mine are thine, and thine are mine; and I am glorified in them." (John 17:1, 2, and 8-10)
-TurretinFan
