Man has sinned. Man is in sin. Man needs to atone for his sins. Big stop. Man can’t adequately atone for his sins. First off, because how could he ever repay the debt that he owes God? Second, how could a man make perfect penance to atone for that sin?
God is perfect. God can make perfect penance, but God, in his own nature cannot suffer and die.
Because man offends God, man must atone. However, only God can do this. So, the Second Person of the Trinity had to take on a human form (the Incarnation) in order to do it. Jesus, as man, can atone for our sins, and Jesus as God, can do it perfectly.
That’s a short summary of the way that C.S. Lewis explains it in Mere Christianity. It may not be quite the Catholic position (I don’t know), but perhaps it is a good place to start.
And perhaps Hebrews 9 would help:
11 But when Christ came as high priest of the good things that have come to be, passing through the greater and more perfect tabernacle not made by hands, that is, not belonging to this creation, 12 he entered once for all into the sanctuary, **not with the blood of goats and calves but with his own blood, thus obtaining eternal redemption. **13 For if the blood of goats and bulls and the sprinkling of a heifer’s ashes can sanctify those who are defiled so that their flesh is cleansed, 14 **how much more will the blood of Christ, who through the eternal spirit offered himself unblemished to God, cleanse our consciences from dead works to worship the living God. ****15 **For this reason he is mediator of a new covenant: since a death has taken place for deliverance from transgressions under the first covenant, those who are called may receive the promised eternal inheritance. *16 **Now where there is a will, the death of the testator must be established. **17 **For a will takes effect only at death; it has no force while the testator is alive. **18 *Thus not even the first covenant was inaugurated without blood. 19 When every commandment had been proclaimed by Moses to all the people according to the law, he took the blood of calves (and goats), together with water and crimson wool and hyssop, and sprinkled both the book itself and all the people, 20 saying, “This is ‘the blood of the covenant which God has enjoined upon you.’” 21 In the same way, he sprinkled also the tabernacle and all the vessels of worship with blood. **22 **According to the law almost everything is purified by blood, and without the shedding of blood there is no forgiveness. 23 Therefore, it was necessary for the copies of the heavenly things to be purified by these rites, but the heavenly things themselves by better sacrifices than these.
Remember that Jesus came to ‘fulfill the Law.’ Note that the sacrifice of other animals could not forgive sins:Hebrews 10
3 But in those sacrifices there is only a yearly remembrance of sins, 4 for it is impossible that the blood of bulls and goats take away sins.
Christ’s blood could forgive sin. Hence, Christ fulfilled the Law by his blood and his sacrifice, which nothing else could do and which we all needed.