Every student of the Bible knows that in Genesis 3:15 God promised a Savior to Adam and Eve. From that time until Jesus appeared on the Earth, Satan has known the plan as revealed in the Bible and has sought to create alternate Anti-Christs. He will succeed in creating his best yet during the coming judgment.
So it comes as no great surprise to the believer that there are many different people that would have similar characteristics to what Jesus had.
And yet the sheer volume of the prophesies that Jesus fulfilled, and the detail to which He fulfilled them can only fit him.
I can pick any set of traits that I may have in common with someone else. But I am not that person.
As for the argument of embellishment—if anyone tried it, there were contemporaries present that would have shouted down the documents and declared they were false.
This is a very weak argument indeed.