Simple Syllogism.
1. The oldest Gospel, Mark didn’t contain a narrative on the birth of Jesus.
2. Luke and Matthew each contain a (variant) narrative on the birth of Jesus.
3. The birth of Jesus is a pious story.
Conclusion: The narratives about Jesus’ birth were added to supplment the narratives contained in the older narrative of Mark.
Of course SOME people think that particular Pious Story is true. You may, or may not. One of the nice things about logic is my opinion on the issue doesn’t matter if the facts are as I stated them, and my reasoning is correct.
In other words you have no source other than yourself.
And your evidence that the birth narrative is a story rather than an accurate account is?