Mmmh, well, to the effects of this topic, Luke wrote his gospel and the book of Acts. If you want to discuss that I guess we need to open other topic.
This is how the Gospel of Luke starts:
Luke 1:1 Seeing that many have undertaken to compile an account of the facts that are given full credence among us, 2 just as these were handed down to us by those who from the beginning were eyewitnesses and attendants of the message, 3 I resolved also, because I have traced all things from the start with accuracy, to write them to you in logical order, most excellent The·ophʹi·lus, 4 so that you may know fully the certainty of the things that you have been taught orally.
5 In the days of Herod, king of Ju·deʹa, there was a priest named Zech·a·riʹah of the division of A·biʹjah. His wife was from the daughters of Aaron, and her name was Elizabeth ...
Can you recognize historicity in that beginning?
No, I really don't. I see a veneer of credibility with no specifics. Who were these eyewitnesses? Which of them provided which details?
Secondly, why did you stop there?
"Now at the time of the incense offering, the whole assembly of the people was praying outside. Then there appeared to him an angel of the Lord, standing at the right side of the altar of incense...."
Thereafter ensues a story where the angel prophesies the birth of John the Baptist to Zechariah's elderly wife. When Zechariah doesn't believe the angel, the angel magically curses him with muteness.
The story doesn't get any more plausible from there.
You can see why people would regard such stories as...rather unlikely, yes?