Why is it so difficult for intelligent
and informed Christians to recognize
- and openly and publicly admit that -
the Bible is NOT free of all errors?.

The discrepancies in the genealogy of Jesus is a great example of the lengths to which bible apologists will go to deny the obvious.  Some claim, for example that Luke's version differs from Matthew's because Luke traces the lineage through Jesus' mother Mary (who is the only biological parent in this case), while Matthew's chapter traces the lineage through Jesus' father (though he was only the putative father in this case).  This is blattantly false, not only because lineage was always traced through the father, but Luke is as clear as Matthew that their genealogical lineage is from King David to Jesus through Joseph. Now because Luke's genealogy started with Jesus and moved backward, it is hard to compare his genealogy to Matthew's which started with David and moved in the opposite direction to end with Jesus, I have reworded Luke's genealogy to make it easier to compare with Matthew's:

Although Matthew claimed that "There were fourteen generations in all from Abraham to David, fourteen from David to the exile to Babylon, and fourteen from the exile to the Christ." anybody who can count to fourteen can see that either God or Matthew wasn't very good at counting!

1. David fathered Solomon,
2. who fathered Rehoboam
3. who fathered Abijah
4. who fathered Asa
5. who fathered Jehoshaphat
6. who fathered Jehoram
7. who fathered Uzziah
8. who fathered Jotham
9. who fathered Ahaz
10. who fathered Hezekiah
11. who fathered Manasseh
12. who fathered Amon
13. who fathered Josiah
    (Babylonian exile started)
14. who fathered Jeconiah
15. who fathered Shealtiel
16. who fathered Zerubbabel
17. who fathered Abihud
18. who fathered Eliakim
19. who fathered Azor
20. who fathered Zadok
21. who fathered Akim
22. who fathered Elihud
23. who fathered Eleazar
24. who fathered Matthan
25. who fathered Jacob
26. who fathered Joseph
27. who (didn't father Jesus
    according to the Gospels)

1. David fathered Nathan
   (Solomon's younger brother),
2. who fathered Mattatha,
3. who fathered Menna,
4. who fathered Melea,
5. who fathered Eliakim,
6. who fathered Jonam,
7. who fathered Joseph,
8. who fathered Judah,
9. who fathered Simeon,
10. who fathered Levi,
11. who fathered Matthat,
12. who fathered Jorim,
13. who fathered Eliezer,
14. who fathered Joshua,
15. who fathered Er,
16. who fathered Elmadam,
17. who fathered Cosam,
18. who fathered Addi,
19. who fathered Melki,
20. who fathered Neri,
21. who fathered Shealtiel,
22. who fathered Zerubbabel,
23. who fathered Rhesa,
24. who fathered Joanan,
25. who fathered Joda,
26. who fathered Josek,
27. who fathered Semein,
28. who fathered Mattathias,
29. who fathered Maath,
30. who fathered Naggai,
31. who fathered Esli,
32. who fathered Nahum,
33. who fathered Amos,
34. who fathered Mattathias,
35. who fathered Joseph,
36. who fathered Jannai,
37. who fathered Melki,
38. who fathered Levi,
39. who fathered Matthat,
40. who fathered Heli,
41. who fathered Joseph
42. who (didn't father Jesus
    according to the Gospels)

Matthew 1 & 2 ( NRSV )

18 Now the birth of Jesus the Messiah took place in this way. When his mother Mary had been engaged to Joseph, but before they lived together, she was found to be with child from the Holy Spirit. 19 Her husband Joseph, being a righteous man and unwilling to expose her to public disgrace, planned to dismiss her quietly. 20 But just when he had resolved to do this, an angel of the Lord appeared to him in a dream and said, "Joseph, son of David, do not be afraid to take Mary as your wife, for the child conceived in her is from the Holy Spirit. 21 She will bear a son, and you are to name him Jesus, for he will save his people from their sins." 22 All this took place to fulfill what had been spoken by the Lord through the prophet:
        23 "Look, the virgin shall conceive and bear a son, and they shall name him Emmanuel," which means, "God is with us." 24 When Joseph awoke from sleep, he did as the angel of the Lord commanded him; he took her as his wife, 25 but had no marital relations with her until she had borne a son; and he named him Jesus.

2 In the time of King Herod, after Jesus was born in Bethlehem of Judea, wise men from the East came to Jerusalem, 2 asking, "Where is the child who has been born king of the Jews? For we observed his star at its rising, and have come to pay him homage." 3 When King Herod heard this, he was frightened, and all Jerusalem with him; 4 and calling together all the chief priests and scribes of the people, he inquired of them where the Messiah was to be born. 5 They told him, "In Bethlehem of Judea; for so it has been written by the prophet:
       6 'And you, Bethlehem, in the land of Judah, are by no means least among the rulers of Judah; for from you shall come a ruler who is to shepherd my people Israel.'"
       7 Then Herod secretly called for the wise men and learned from them the exact time when the star had appeared. 8 Then he sent them to Bethlehem, saying, "Go and search diligently for the child; and when you have found him, bring me word so that I may also go and pay him homage." 9 When they had heard the king, they set out; and there, ahead of them, went the star that they had seen at its rising, until it stopped over the place where the child was. 10 When they saw that the star had stopped, they were overwhelmed with joy. 11 On entering the house, they saw the child with Mary his mother; and they knelt down and paid him homage. Then, opening their treasure chests, they offered him gifts of gold, frankincense, and myrrh. 12 And having been warned in a dream not to return to Herod, they left for their own country by another road.

13 Now after they had left, an angel of the Lord appeared to Joseph in a dream and said, "Get up, take the child and his mother, and flee to Egypt, and remain there until I tell you; for Herod is about to search for the child, to destroy him." 14 Then Joseph got up, took the child and his mother by night, and went to Egypt, 15 and remained there until the death of Herod. This was to fulfill what had been spoken by the Lord through the prophet, "Out of Egypt I have called my son."

16 When Herod saw that he had been tricked by the wise men, he was infuriated, and he sent and killed all the children in and around Bethlehem who were two years old or under, according to the time that he had learned from the wise men. 17 Then was fulfilled what had been spoken through the prophet Jeremiah:
       18 "A voice was heard in Ramah, wailing and loud lamentation,Rachel weeping for her children; she refused to be consoled, because they are no more."

19 When Herod died, an angel of the Lord suddenly appeared in a dream to Joseph in Egypt and said, 20 "Get up, take the child and his mother, and go to the land of Israel, for those who were seeking the child's life are dead." 21 Then Joseph got up, took the child and his mother, and went to the land of Israel. 22 But when he heard that Archelaus was ruling over Judea in place of his father Herod, he was afraid to go there. And after being warned in a dream, he went away to the district of Galilee. 23 There he made his home in a town called Nazareth, so that what had been spoken through the prophets might be fulfilled, "He will be called a Nazarean."

Luke 2 ( NRSV )

2 In those days a decree went out from Emperor Augustus that all the world should be registered. 2 This was the first registration and was taken while Quirinius was governor of Syria. 3 All went to their own towns to be registered. 4 Joseph also went from the town of Nazareth in Galilee to Judea, to the city of David called Bethlehem, because he was descended from the house and family of David. 5 He went to be registered with Mary, to whom he was engaged and who was expecting a child. 6 While they were there, the time came for her to deliver her child. 7 And she gave birth to her firstborn son and wrapped him in bands of cloth, and laid him in a manger, because there was no place for them in the inn.

8 In that region there were shepherds living in the fields, keeping watch over their flock by night. 9 Then an angel of the Lord stood before them, and the glory of the Lord shone around them, and they were terrified. 10 But the angel said to them, "Do not be afraid; for see�I am bringing you good news of great joy for all the people: 11 to you is born this day in the city of David a Savior, who is the Messiah, the Lord. 12 This will be a sign for you: you will find a child wrapped in bands of cloth and lying in a manger." 13 And suddenly there was with the angel a multitude of the heavenly host, praising God and saying,
       "Glory to God in the highest heaven,
        and on earth peace among those whom he favors!" 15 When the angels had left them and gone into heaven, the shepherds said to one another, "Let us go now to Bethlehem and see this thing that has taken place, which the Lord has made known to us." 16 So they went with haste and found Mary and Joseph, and the child lying in the manger. 17 When they saw this, they made known what had been told them about this child; 18 and all who heard it were amazed at what the shepherds told them. 19 But Mary treasured all these words and pondered them in her heart. 20 The shepherds returned, glorifying and praising God for all they had heard and seen, as it had been told them.

21 After eight days had passed, it was time to circumcise the child; and he was called Jesus, the name given by the angel before he was conceived in the womb. Jesus Is Presented in the Temple
       22 When the time came for their purification according to the law of Moses, they brought him up to Jerusalem to present him to the Lord 23 (as it is written in the law of the Lord, "Every firstborn male shall be designated as holy to the Lord"), 24 and they offered a sacrifice according to what is stated in the law of the Lord, "a pair of turtledoves or two young pigeons."

39 When they had finished everything required by the law of the Lord, they returned to Galilee, to their own town of Nazareth. 40 The child grew and became strong, filled with wisdom; and the favor of God was upon him.

Contrast between the two birth stories:

Matthew 1 & 2

Luke 2

"Who made me a judge?."(Luke 12:14)
"I did not come to judge but to save."(John 12:47)
"God did not send the Son to judge the world."(John 3:17)

"I judge no one."(John 8:15).