First of all, pagan and polytheistic are not the same thing, and pagan can have several different meanings. I mean it in this headline to refer to those polytheistic religions which existed before the Roman Empire adopted Christianity as its official religion, and which would survive in various forms to this very day. By this definition, Christian cannot mean pagan. Whether or not Christianity is polytheistic is another can of worms entirely. Many Muslims and Jews agree that the insistence upon the Trinity precludes most Christians (at least the vast majority of whom agree with the Council of Nicea) from being monotheistic.

I would disagree that there is nothing unique about Christianity - that's a blanket statement that no serious scholar would take seriously. It has certainly been influenced by cultures and has in turn, influenced cultures it has come to (or most likely, forced upon).

And your over-simple reason may be true, but it's not necessarily supported by evidence. Stuff indeed does not "just happen," but here, we look for documentable reasons as to why "stuff happens."