Qur’an 6:164—Say, “Shall I seek a Lord, other than Allah while He is the Lord of all things?” And no soul earns evil but only against itself; nor does any bearer of burden bear the burden of another. Then to your Lord will be your return, and He will inform you of that wherein you used to differ.
Qur’an 17:13-15—And We have fastened every man's deeds to his neck, and on the Day of Resurrection, We shall bring out for him a book which he will find wide open. (It will be said to him): “Read your book. You yourself are sufficient as a reckoner against you this Day.” Whoever goes right, then he goes right only for the benefit of his own self. And whoever goes astray, then he goes astray to his own loss. No one laden with burdens can bear another's burden. And We never punish until We have sent a Messenger (to give warning).
Interestingly, however, the Qur'an contradicts itself on this point, for other verses plainly declare that some people will indeed bear the burdens of others:
Qur’an 16:22-25—Your God is one God; so (as for) those who do not believe in the hereafter, their hearts are ignorant and they are proud. Truly Allah knows what they hide and what they manifest; surely He does not love the proud. And when it is said to them, what is it that your Lord has revealed? They say: Stories of the ancients; That they may bear their burdens entirely on the day of resurrection and also of the burdens of those whom they lead astray without knowledge; now surely evil is what they bear.
The Qur'an even contradicts itself in the space of two verses, claiming in 29:12 that disbelievers will not bear the burdens of others, and in 29:13 that disbelievers will bear the burdens of others!
Qur’an 29:12-13—And those who disbelieve say to those who believe: “Follow our way and we will verily bear your sins,” never will they bear anything of their sins. Surely, they are liars. And verily, they shall bear their own loads, and other loads besides their own, and verily, they shall be questioned on the Day of Resurrection about that which they used to fabricate.
But it gets worse for Muslims who object to Jesus' sacrifice, for Muhammad himself declared that Allah will punish Jews and Christians for the sins of Muslims:
Sahih Muslim 6665—Abu Musa reported that Allah's Messenger said: When it will be the Day of Resurrection Allah would deliver to every Muslim a Jew or a Christian and say: That is your rescue from Hell-Fire.
Sahih Muslim 6666—Allah’s Apostle said: No Muslim would die but Allah would admit in his stead a Jew or a Christian in Hell-Fire.
Sahih Muslim 6668—Allah’s Messenger [said]: There would come people amongst the Muslims on the Day of Resurrection with as heavy sins as a mountain, and Allah would forgive them and He would place in their stead the Jews and the Christians.
110 Hadith Qudsi—Allah’s Messenger said: On the Day of Resurrection, my Ummah (nation) will be gathered into three groups. One sort will enter Paradise without rendering an account (of their deeds). Another sort will be reckoned an easy account and admitted into Paradise. Yet another sort will come bearing on their backs heaps of sins like great mountains. Allah will ask the angels though He knows best about them: Who are these people? They will reply: They are humble slaves of yours. He will say: Unload the sins from them and put the same over the Jews and Christians: then let the humble slaves get into Paradise by virtue of My Mercy.
Hence, if Muslims believe that it would be unjust and unfair for God to punish someone for the sins of others, then Muslims must reject Muhammad, for he claimed that Muslims with sins "as heavy as a mountain" will enter paradise and receive their virgins, because Allah will place their mountainous sins on the backs of Christians and Jews.
Compare this with the Christian claim that Jesus willingly pays the price for the sins of others, and you will see the real difference between Christianity and Islam. In Christianity, God loves us so much that he enters creation to meet the requirements of his perfect justice. In Islam, God hates unbelievers so much that he punishes them even for the sins of Muslims.
Of course, Muslims are still influenced by passages of the Qur'an declaring that "no bearer of burden shall bear the burden of another." However, they would do well to notice what these verses actually say. The Qur'an does not say that "no one" can bear the burdens of another. Instead, it claims that "no bearer of burden" (i.e. no one who already has a burden of sin) shall bear the burden of another. In other words, if someone already has a burden of sin, this person can't bear the burdens of other people, for he has his own sins to deal with. This leaves the door wide open, however, for someone who is completely sinless (someone who has no burden of sin) to willingly bear the burdens of others.
Ironically, then, the Christian view is fair and just according to the Qur'an, while Muhammad's view is unfair and unjust!
If only Muslims would read their sources, they would have to abandon this objection to Christianity!
Here are some articles by Sam Shamoun for further reading: