If two disparate cultures, half a world and a full millenium separated, come up with the same idea, does this mean they were copying each other? No. It certainly doesn't mean the older culture copied the younger culture.
My sister is reading a book against Christianity. One of the points it made is that the concept behind communion, eating God, was borrowed from the Aztecs. How could Christians have borrowed something from a culture that didn't exist? It couldn't have. That's a totally fallacious argument.
It pointed to things in other cultures that are similar to Christianity and said that Christianity “borrowed” those. The use of iron came up at the same time in different places. Which one borrowed from the other? And if the use of iron could be discovered separately in disparate places, why couldn't symbols of Christianity?
The book is arguing against the symbols Christians use.
Someone else used disks around heads to tell you the person depicted was special. So what? That doesn't disprove Christianity. Even if they did borrow the idea from the Egyptians, haloes around saints' heads is NOT in the Bible. There are no pictures in any of the earliest manuscripts. That was art and added later.
The Romans had a midwinter festival which the Christian church took and turned into the Christmas festival, celebrating the birth of Christ. So what? There's nothing in the Bible that says when Jesus was born. So let's pick a random day. We have all these pagan converts who are used to a midwinter celebration and I'd like something fun to do then, too, so we pick the middle of winter. No one in all of Christendom has ever said that December 25 was Christ's actual birthdate. (At least not as far as I know and certainly no one now should.)
The book also argues that the canonization of the saints in the Catholic church comes from an Egyptian religious ceremony. First, how do they know? Does anyone know who started the canonization process and what information was in their heads and their libraries? No. Second, even if they did, so what? The Catholic church is not the Bible and the Bible doesn't say anything about canonization of the saints.