Parents are not to be put to death for their children, nor children put to death for their parents; each will die for their own sin. -Deuteronomy 24:16The idea that Christ died as if He commited our sin violates the Biblical teaching that each man be put to death for his OWN sins. This verse, however, seems to only apply to adults, since young children in the Bible are put to death, or killed, because of their parents sins, as in the case of David's son, or the nations God commanded the Israelites to destroys. Regardless, Christ could not have been put to death for the sins of others (at least justly!). Rather, Christ willingly laid down His own life for the sake of others, not that He should die as their substitute, but that by His righteous death, God would show mercy to mankind, thus allowing man forgiveness on the condition they repent of their sins. After all, Christ did make several warning statements that certain sins would cause the soul to go to Hell forever, as we see in Matthew 5 with sexual sins, Matthew 6 with withholding forgiving your brother's sins and so on.
On another point, Deuteronomy 24:16 is a verse anti/counter-Missionary Jews use against Christians. Their claim is legitimate, but only against baptistic and Calvinistic types of Christians that espouse this particular view of the atonement that says "Christ died in our place" or "He took the wrath of God in our place" and so on. Rather, the Biblical Christ was a propitiation for the sins of the world, meaning His death provided MERCY for mankind.
I have already written before that the idea of a penal substitution when logically followed out is a denial of Trinitarianism, or can be an affirmation of a sort of Arianism (since God cannot be forsaken by God), or some form of theology where Christ as a man and Christ as God are divorced (undoing the incarnation).
Calvinists try to prove a penaly substitution with verses like 2 Corinthians 5:21, or Isaiah 53 and so on. When the fact is 2 Corinthians 5:21 by saying Christ "became sin for us" is an expression St Paul was using for a sin offering, and Isaiah 53 doesn't mean God treated Christ as if He had our sins, in fact Matthew 8:17 interprets this part of Isaiah as Jesus healing the sick and casting out demons:
When it was evening, they brought him many who were possessed by demons, and he drove out the spirits by a word and cured all the sick, to fulfill what had been said by Isaiah the prophet: “He took away our infirmities and bore our diseases.”--Matthew 8:16-17