When somebody living under the Torah sinned they were responsible for what they had done, but if they repented they could be forgiven by a sacrifice that would bear their sin before God. The Torah explains this:
He must bring as his offering for the sin he committed a female goat without defect. He is to lay his hand on the head of the sin offering and slaughter it at the place of the burnt offering. Then the priest is to take some of the blood with his finger and put it on the horns of the altar of burnt offering and pour out the rest of the blood at the base of the altar. He shall remove all the fat, just as the fat is removed from the fellowship offering, and the priest shall burn it on the altar as an aroma pleasing to the LORD. In this way the priest will make atonement for him, and he will be forgiven. ” Leviticus 4:28-31, NIV
For the life of a creature is in the blood, and I have given it to you to make atonement for yourselves on the altar; it is the blood that makes atonement for one’s life. ” Leviticus 17:11, NIV
The Torah teaches individual responsibility and forgiveness through a substitute sacrifice that bears our sin. That exactly was what Jesus did, He died in our stead. He was the sacrifice for the whole world sins on that cross.
In the book of the prophet Ezekiel we see this idea as well.
(The priests) will put the most holy offerings (there) ” the grain offerings, the sin offerings and the guilt offerings ” for the place is holy. ” Ezekiel 42:13, NIV
Therefore Muslims are not reading Deuteronomy 24:16 or Ezekiel 18:20 in their context (which is not news to me since that’s the only way for them to attack the Bible which by the way was confirmed by their own false prophet Muhammad to be authentic ” Qur’an 3:3). These verses are not saying there is no sacrifice that can bear our sin. Instead they are saying that we are individually responsible for our sins and need to seek forgiveness through God’s provision of a substitute sacrifice that can bear our sin. These verses do not support Islam at all; instead they confirm what Christianity teaches.
The blood of those animals, however, couldn’t permanently wash away sins; they could only cover their sins for a year, that’s why He offered His only begotten Son to shed His spotless, undefiled blood to be the ultimate sacrifice, not only for those who are under the Torah but also the whole world:
11. But Christ having come as a high priest of the coming good things, through the greater and more perfect tabernacle, not made with hands, that is to say, not of this creation, 12. nor yet through the blood of goats and calves, but through his own blood, entered in once for all into the Holy Place, having obtained eternal redemption. 13. For if the blood of goats and bulls, and the ashes of a heifer sprinkling those who have been defiled, sanctify to the cleanness of the flesh: 14. how much more will the blood of Christ, who through the eternal Spirit offered himself without defect to God, cleanse your conscience from dead works to serve the living God? 15. For this reason he is the mediator of a new covenant, since a death has occurred for the redemption of the transgressions that were under the first covenant, that those who have been called may receive the promise of the eternal inheritance. 16. For where a last will and testament is, there must of necessity be the death of him who made it. 17. For a will is in force where there has been death, for it is never in force while he who made it lives. 18. Therefore even the first covenant has not been dedicated without blood. 19. For when every commandment had been spoken by Moses to all the people according to the law, he took the blood of the calves and the goats, with water and scarlet 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 commanded you.” 21. Moreover he sprinkled the tabernacle and all the vessels of the ministry in the same way with the blood. 22. According to the law, nearly everything is cleansed with blood, and apart from shedding of blood there is no remission. ” Hebrews 9:11-22, WEB