Why can we not accept that Jesus (as) died to atone for our sins?

Because God forgave people long before Jesus (as) and all over the world. Forgiveness never depended on a sacrifice, but on repentance and a life lived by God's guidance, and no one bears the burden of another.

This question is really not about what we accept, but about what God accepts. He alone decides whether He accepts a sacrifice and how He forgives. So it is worth looking at how God has acted throughout history.

Before Jesus (as) was born, the world did not know him. Even afterwards he remained unknown on most continents for many centuries. If forgiveness were possible only through faith in his sacrificial death, what became of all the people before him? And what of the many whom his message never reached? It would be hard to understand why God should have hidden something so decisive from almost all of humanity for so long. Moses (as) did not proclaim anything of the kind to his people either.

This leads to a simple question. Did God forgive anyone before Jesus (as), or not? If He did, then his death was evidently not necessary for forgiveness. God has always forgiven those who repented and followed the example of God-fearing people. That has always been His law.

The first verse above fits this. No soul bears the burden of another. It would not be just to make an innocent person suffer for the guilt of others. God needs no such sacrifice in order to forgive. The second verse shows how near His forgiveness is to every person who turns to Him.

So for Muslims Jesus (as) remains a highly honoured prophet and an example. Salvation is found by following his example, not by placing one's sins upon him.