The question, as stated, presents an misunderstood view of the economy of salvation. And although it is ultimately a mystery, we can say a fair amount about sin and salvation that makes Christ's sacrifice more reasonable sounding, and the possibility of "self-salvation" far less reasonable sounding. In essence, God created humans to be like God, humans thought they were getting short-changed and disobeyed God (His Word, the law of life), so God had to become fully human to make humans like God again.
First, God makes man in His image. We can see this directly in scripture. As creation culminates, God creates man and woman.
God created mankind in his image; in the image of God he created them;
male and female he created them. (Genesis 1:3)
Second, God places man and woman in the Garden of Eden, the Garden of delight. He gives them dominion over everything except the prerogative of good and evil. Based on context, this could mean divinity itself. The Catholic read on this, as I understand it, is that humanity is initially created in a state wherein they will live joyfully and forever, provided that trust in God's exclusive right to determine good versus evil and who is entitled to what.
15 The LORD God then took the man and settled him in the garden of
Eden, to cultivate and care for it. 16 The LORD God gave the man this
order: You are free to eat from any of the trees of the garden 17
except the tree of knowledge of good and evil. From that tree you
shall not eat; when you eat from it you shall die. (Genesis 2:15-17)
Third, mankind starts to believe that God is holding out. They believe that, although they were told they were made in God's image, that they actually far from God-like. They believe that they must take matters into their own hands, and they taste the forbidden fruit.
1 Now the snake was the most cunning of all the wild animals that the
LORD God had made. He asked the woman, “Did God really say, ‘You shall
not eat from any of the trees in the garden’?” 2 The woman answered
the snake: “We may eat of the fruit of the trees in the garden; 3 it
is only about the fruit of the tree in the middle of the garden that
God said, ‘You shall not eat it or even touch it, or else you will
die.’” 4 But the snake said to the woman: “You certainly will not die!
5 God knows well that when you eat of it your eyes will be opened and
you will be like gods, who know good and evil.” 6 The woman saw that
the tree was good for food and pleasing to the eyes, and the tree was
desirable for gaining wisdom. So she took some of its fruit and ate
it; and she also gave some to her husband, who was with her, and he
ate it. 7 Then the eyes of both of them were opened, and they knew
that they were naked; so they sewed fig leaves together and made
loincloths for themselves. (Genesis 3:1-7)
At this point, all humans are destined to die. People are finite and stupid, for one. And our pride destines us to die. We simply don't know what it means to be Godlike, nor do we have the power to acquire Godliness. We don't even fully understand what good and evil are, let alone the power to enact good. Least of all do we understand the full consequences of our actions, nor have the power to understand. Hence, having taken good and evil into our own hands, we cannot fulfill God's purpose for us to be like Him. We simply don't have the ability to raise ourselves to Godliness.
Fourth, God rescues mankind. And since the original plan was for humans to be like God, God can accomplish this by entering the full human experience. From birth:
10 The angel said to them, “Do not be afraid; for behold, I proclaim
to you good news of great joy that will be for all the people. 11 For
today in the city of David a savior has been born for you who is
Messiah and Lord. 12 And this will be a sign for you: you will find an
infant wrapped in swaddling clothes and lying in a manger.” (Luke 2:10-12)
Through daily life, learning, teaching, eating, partying, friendship, betrayal, judgement, and denial to suffering, agony, mockery, and death.
Jesus cried out in a loud voice, “Father, into your hands I commend my
spirit”; and when he had said this he breathed his last. (Luke
And the Catholic understanding of this is twofold.
Firstly, we understand that Christ makes humans like God again by bringing the fullness of God into the full human experience. This is often called divinization or deification. Because Jesus was fully God, everything that He was as a human, all that happened to Him, and all that He did is God-like, including death, which we are bound to!
The Son of God became man so that we might become God.
- St. Athanasius
Not coincidentally, Jesus is risen from the dead, suggesting in a very "loud" manner that we too can be risen. But not of our own doing! Only by accepting God's offer for salvation by "commending our spirit" to God! That is, we can only allow ourselves to be risen by God by allowing God's offer, the power of the cross, to make us like Him again. We cannot do it on our own, for we are not God. It is precisely in an attempt to "do it on our own" that we are apart from God.
But secondly, and contrary to your request for this question, we understand that the mechanics of salvation are a mystery! It's well and good to talk about deification. It's well and good to say that Christ became sin, as we often do. It's well and good to talk about paschal sacrifices, the law, the Word Made Flesh, etc. But, that doesn't mean we understand it. And if we start to presume salvation and God are not mysterious, we find ourselves back in front of the forbidden fruit, ready to take that ill-advised bite.