I agree with what you wrote but not every Biblical contradiction is so easily dismissed. Good luck weaving the two birth narratives into one.It would be stranger still if all 4 Gospels repeated the same supposed eyewitness accounts in a "verbatim" manner. That would make it appear that there was some coaching going on.......all were reading from a script.
What? Are humans part of a "collective" mentality seeing everything as one, with everyone noticing "exactly" the same facts? Even in a court room you could have 5 witnesses to the same crime and each witness would present visible facts not noticed by the other 4 witnesses......or present some information that others assumed to be unimportant.
There is a important rule of law to remember. Adding extra information or substracting information from an eyewitness accout does not equal a fabrication, each person is an individual with different traits of observation that can be effected by eyesight, nerves, health.....etc., attention to detail, lack of attention to detail. There have been cases where even the color of clothing and hair were each testified as being different......but each person told that truth as they rememered. One had mistaken the color of hair as being read because all he noticed was the big red 1 on the baseball cap being worn......another stated the subject wore all blue......another black.......why? The subject was wearing a blue coat that he removed in order to run faster....etc.,
Example: Suppose you or someone else was repeating the events of how you and your wife witnessed a crime while shopping at the local mall. Your first question is the same one asked of your wife by the prosecutinig attorney. "Why were you at the mall on this day?" You answer, "I came along with the wife in order to purchase hunting supplies and a few cinnamon rolls..........there is this one little bakery that makes the very best pasteries.....". Your wife replies by telling the prosecutor about how this mall has great clothing stores.....
Both of you begin to tell your story about one certain event that occured at the same mall, on the same day......but each provided different details about as to why you and your wife were there on that particular day.......
Did you or your wife either........contradict the other's testimony?
The same is true of the Gospels........each told by someone with a different view point. In one account the author tells of there being 3 angels.....another remembers seeing only 2 angels at the grave of Jesus. Is this a contradiction? Of course not........there are many reasons as to why one mentions 3 another only 2......perhaps they arrived at slightly different times of day.....one angel has already gone and one witness had a glance at only 2 angels that were wittnessed existing the scence...etc., the first witness arrived much eariler than the latter witness and the actual scene changed in perception and reality.
This is just one example as to why some claim the Bible contracts itself. This is exactly the case between 2 different gospels accounts as to how many angels were seen at the grave of Jesus. 2 different numbers. But when you actually read of the 2 different accounts the passages actually document different time frames of each witnessed account.
I think its wrong to read it as history and not what it is, theology.