Chapter 9: The Atonement of Jesus Christ, C: Only Jesus Christ possessed the qualifications and attributes necessary to perfrom an infinite atonement

The Savior was the only one who could perform the atonement because of his unique traits. First, he was the Only Begotten son of the father, meaning he had power over his body that we do not have. This allowed him to suffer the pain of the atonement when another would have died or been succumbed by the pain.

Wherefore, the Almighty God gave his Only Begotten Son, as it is written in those scriptures which have been given of him.
D&C 20:21

Which suffering caused myself, even God, the greatest of all, to tremble because of pain, and to bleed at every pore, and to suffer both body and spirit - and would that I might not drink the bitter cup, and shrink.
D&C 19:18

Behold, they believed in Christ and worshiped the Father in his name, and also we worship the Father in his name. And for this intent we keep the law of Moses, it pointing our souls to him; and for this cause it is sanctified unto us for righteousness, even as it was accounted unto Abraham in the wilderness to be obedient unto the commands of God in offering up his son Isaac, which is a similitude of God and his Only Begotten Son.
Jacob 4:5

The Savior was completely sinless. He was a perfect sacrifice because he had no sin in him. This is not because he had it easy or didn't go through the same, but rather he went through everything yet still remained clean.

And ye know that he was manifested to take away our sins; and in him is no sin.
1 John 3:5

For we have not an high priest which cannot be touched with the feeling of our infirmities; but was in all points tempted like as we are, yet without sin.
Hebrews 4:15

Listen to him who is the advocate with the Father, who is pleading your cause before him--Saying: Father, behold the suffering and death of him who did no sin, in whom thou wast well pleased; behold, the blood of thy Son was shed, the blood of him whom thou gavest that thyself might be glorified. Wherefore, Father, spare these my brethren that believe on my name, that they may come unto me and have everlasting life.
D&C 45:3-5

Some superior agency was needed to elevate [fallen man] above his low and degraded position. This superior agency was the Son of God, who had not, as man had, violated a law of His Father, but was yet one with His Fatherk, possessing His glory, His power, His authority, His dominion.
John Taylor, The Mediation and Atonement, 145

Christ had power over death. He was able to hold on to his life or let it go. When he suffered and died for us, it was entirely by his active choice.

For as the Father hath life in himself; so hath he given to the Son to have life in himself.
John 5:26

Therefore doth my Father love me, because I lay down my life, that I might take it again. No man taketh it from me, but I lay it down of myself. I have power to lay it down, and I have power to take it again. This commandment have I received of my Father.
John 10:17-18