Sacrifice is the gift of one life for another. The one who sacrificed himself has lost something for the good of others. It is the manifestation of love or the sense of duty; Jesus Christ by sacrificing himself manifested his love for humanity; on the other hand by telling the people of Israel to use blood in order to be spared was a duty of God to tell them and for them to do so otherwise they would all be struck by the same misfortune (death of the firstborn) despite God's love for them. When God wanted to kill the firstborn of Egypt, God defined a clear rule to follow to escape the carnage. It was a question of sacrificing a lamb or a kid in place of the firstborn who was to die; Exodus 12: 3 Speak to all the assembly of Israel, and say: On the tenth day of this month a lamb shall be taken for each family, a lamb for each house. 4 If the house is too few for a lamb, he will be taken with his nearest neighbor, according to the number of the people; you will count for this lamb according to what each one can eat. 5 It shall be a lamb without blemish, male, a year old; you can take a lamb (priority) or a kid (for those who do not have sheep). 6 You shall keep it until the fourteenth day of this month; and all the congregation of Israel shall sacrifice him between the two evenings. 7 They will take some of its blood and put it on the two doorposts and on the lintel of the door of the houses where they will eat it. 8 This same night the flesh shall be eaten, roasted in the fire; it shall be eaten with unleavened bread and bitter herbs. 9 You shall not eat it half-cooked and boiled in water; but it will be roasted in the fire, with the head, the legs and the inside. 10 You shall leave none of it until the morning; and if there is anything left in the morning, you will burn it in the fire. 11 When you eat it, you will have your loins girded, your shoes on your feet, and your staff in your hand; and you will eat it in haste. It is the Lord's Passover. 12 That night I will pass through the land of Egypt, and I will strike down all the firstborn in the land of Egypt, from man to beast, and will execute judgment against all the gods of the land. Egypt. I am the Lord. 13 The blood will be a sign to you on the houses where you are; I will see the blood, and I will pass over you, and there shall be no plague to destroy you, when I smite the land of Egypt.
When the command was given to Moses, he carried it to the people and followed exactly what they were to do; 21 Moses called all the elders of Israel, and said to them, Go and get livestock for your families, and sacrifice the Passover. 22 Then take a bunch of hyssop and dip it in the blood that is in the basin, and touch the lintel and the two doorposts with the blood that is in the basin. None of you shall leave your house until morning. 23 When the LORD passes by to strike Egypt, and sees the blood on the lintel and on the two doorposts, the LORD will pass over the gate, and will not allow the destroyer to come into your houses to strike . 24 You shall observe this as a law for you and for your children forever.
The Israelites obeyed the voice of God to be saved: 28 And the children of Israel went and did as the LORD commanded Moses and Aaron; they did so. 29 In the middle of the night the LORD struck down all the firstborn in the land of Egypt, from the firstborn of Pharaoh who sat on his throne, to the firstborn of the captive in his prison, and even to all the firstborn animals. 30 Pharaoh rose up by night, he and all his servants, and all the Egyptians; and there was a great cry in Egypt, for there was not a house where there was not a dead man. 31 That same night Pharaoh called Moses and Aaron, and said to them, Arise, come out from among my people, you and the children of Israel. Go, serve the LORD, as you have said. 32 Take your sheep and your oxen, as you said; go, and bless me.
Jesus Christ is the first born who was represented by the Passover lamb. He was sacrificed for them and for us; Hebrews 1:6 And when he brought the firstborn into the world again, he said, Let all the angels of God worship him. 7 Moreover he says of the angels: He who makes his angels winds, and his servants a flame of fire. 8 But he said to the Son, Your throne, O God, is eternal; The scepter of your reign is a scepter of equity; 9 You have loved righteousness, and have hated iniquity; Therefore, O God, your God has anointed you with the oil of joy above your equals.
It is not accidental that God asked Abraham to sacrifice his son. He himself had already done this act; Genesis 22:9 When they came to the place that God had told him, Abraham built an altar there, and arranged the wood. He bound his son Isaac, and placed him on the altar on top of the wood. 10 Then Abraham stretched out his hand and took the knife to kill his son. 11 Then the angel of the LORD called to him from heaven, and said, Abraham! Abraham! And he answered: Here I am! 12 And the angel said, Stretch not thine hand upon the child, nor do any thing unto him; for now I know that you fear God, and have not withheld your only son from me. 13 Abraham lifted up his eyes, and saw behind him a ram held in a bush by its horns; and Abraham went and took the ram, and offered it as a burnt offering in place of his son.
God bless you !