There are a few issues with the story of the Nativity that happens in Matthew and then follows in Luke. Let us look at the original to start off with. This is the Holman Christian Standard Bible translation.

Matthew 1:18-25
18 The birth of Jesus Christ came about this way: After His mother Mary had been engaged to Joseph, it was discovered before they came together that she was pregnant by the Holy Spirit. 19 So her husband Joseph, being a righteous man, and not wanting to disgrace her publicly, decided to divorce her secretly.
20 But after he had considered these things, an angel of the Lord suddenly appeared to him in a dream, saying, “Joseph, son of David, don’t be afraid to take Mary as your wife, because what has been conceived in her is by the Holy Spirit. 21 She will give birth to a son, and you are to name Him Jesus, because He will save His people from their sins.”
22 Now all this took place to fulfill what was spoken by the Lord through the prophet:
23 See, the virgin will become pregnant
and give birth to a son,
and they will name Him Immanuel,
which is translated “God is with us.”
24 When Joseph got up from sleeping, he did as the Lord’s angel had commanded him. He married her 25 but did not know her intimately until she gave birth to a son. And he named Him Jesus.

Notice anything that didn’t synch up? The name isn’t the same.

Here’s the footnote to Matthew 1:21 from HCSB – “Jesus is the Gk form of the Hebrew name “Joshua,” which equals “The LORD saves” or “Yahweh saves.””

This makes the angel’s comment in line 21 “…because He will save His people from their sins” make sense. His name is his job description.

But then the prophecy by Isaiah says that they will name him Immanuel, which is translated as “God is with us.”

Which one is it? Jesus (Joshua, Yeshua), meaning “the Lord saves” (The Lord being Yahweh), or is it Immanuel, meaning “God is with us”?

Maybe it is a little of both. God saves us by being with us. God lets us know that we aren’t alone. God isn’t “up there”. God cares so much about us that God came down here to be among us and save us from our fear and loneliness. Our God is a hands-on kind of God. Our God isn’t like a CEO or upper management. Our God knows what we are being asked to do, because our God has done it with us. Our God knows how hard life is here in these bodies with their faults and limitations. Our God knows because our God has lived it with us.

Now, this is a poetic interpretation. It sounds good, but it doesn’t solve the problem.

Is the prophecy fulfilled or not? He wasn’t named Immanuel, and he wasn’t named with the same meaning.

Then there is another problem. Are they married or not? The story continues in Luke 2:1-7. This too is from the HCSB translation.

“In those days a decree went out from Caesar Augustus that the whole empire should be registered. 2 This first registration took place while Quirinius was governing Syria. 3 So everyone went to be registered, each to his own town.
4 And Joseph also went up from the town of Nazareth in Galilee, to Judea, to the city of David, which is called Bethlehem, because he was of the house and family line of David, 5 to be registered along with Mary, who was engaged to him and was pregnant. 6 While they were there, the time came for her to give birth. 7 Then she gave birth to her firstborn Son, and she wrapped Him snugly in cloth and laid Him in a feeding trough—because there was no room for them at the lodging place.”

Note line 5. She was engaged to him. Not his wife. In Matthew 1:24, he married her after the angel talked to him. She hadn’t given birth yet. The story of the birth happens only in Luke, and there she is listed as being engaged, not married.

It is important to read carefully and question everything. If things don’t match up, ask why.