Exercises:
1)  The pattern in Matthew 1:1-17 is "X was the father of Y; Y was the father of Z."  What exceptions or variations are there on this pattern? 
    So:  2) Note verses 3, 5, and 6, which all add the phrase, "whose mother was X."  (If you have an older translation, it may not be immediately clear that this is what is being said -- it may say something like "And Judah begat Perez and Zara of Tamar.")  Who are these four mothers?   Why were these four female ancestors -- and no other -- specifically mentioned?  What do they have in common?  Why are they included?
    Another set of questions, for your imagination:  3) If you believe in the "Annunciation," a divine announcement to Mary of her coming pregnancy, do you believe that Mary's neighbors were also informed of the good tidings?  If you believe the neighbors were not informed, imagine that you are one of these neighbors of Mary's in a small, conservative, provincial village (either Nazareth or Bethlehem).  You learn (or observe) that she is pregnant (remember, you are in a culture which deals very harshly with any kind of extramarital sexual activity, at least for women).  How do you and your other neighbors respond to Mary's condition?  If someone in her family tells you that she is pregnant by God, what -- if anything -- does this do to your attitude toward her?
4)  Why do Mark and John not report on a virgin birth -- nor mention Jesus' birth at all?
5)  Read Mark 6:1-6.  When the villagers ask, "Isn't this the son of Mary?" are they implying that Jesus doesn't have a father?
Discussion:
1) Matthew includes four female ancestors of Jesus.  If you want to read more about them, they are:
   a) Tamar, a Canaanite woman, appearing in Genesis 38, "whose children were born of incest";
   b)  Rahab, a Hittite woman, "the madam of a brothel," whose story is told in Joshua 2;
   c)  Ruth, a non-Israelite, whose story fills the entire book of Ruth, and "who got her second husband by solicitation, if not fornication"; and
   d)  Bathsheba, the "wife of Uriah" the Hittite.  Her story appears in 2 Samuel 11-12; "her relations with David began in adultery, though she became the mother of Solomon."                                                            (Quotes above from Mitchell, 22-23)
2)  What these four ancestresses have in common is that
    a) they were all non-Israelite women, and
    b) they were all involved in some sort of sexual irregularity, whether or not of their own choosing2.  So why does Matthew mention them?  This leads us to an answer to the next question:
3)  Some scholars are inclined to dismiss the infancy narratives as pure fiction, in part because Matthew and Luke, the only two gospel writers to provide them, differ so dramatically on the facts.  Some of these scholars think that Jesus had a perfectly ordinary birth and childhood in Nazareth, to perfectly ordinary parents who were married in a perfectly ordinary way.
But the question then remains:  Why does Matthew in particular seem so obsessed with defending the very subject of sexual irregularity?  Or if this is not what he is doing, why then does he make such a point of the sexual irregularities in the ancestry of Jesus?  Many scholars agree that there were at least rumors -- perhaps by opponents of Christianity -- of Jesus' alleged illegitimacy.  These were current in the second century, and perhaps earlier, perhaps early enough for Matthew to feel a need to both deny them by creating a miraculous infancy narrative and at the same time say, in effect, by his carefully constructed genealogy, that it doesn't matter even if it is true.
    Stephen Mitchell, accepting the view that even during his lifetime Jesus had to endure charges of illegitimacy -- since it could hardly be otherwise for anyone born out of wedlock in such a culture -- says:
   "The first thing we ought to realize about Jesus' life is that he grew up as an illegitimate child.  On this point both traditional Christians and non-Christians can fully agree, because even those who believe in the virginal conception don't believe that the angel Gabriel appeared to everyone else in Nazareth, to assure them that Mary's child had been fathered by God. ... If an angel appeared, he appeared only to Mary, and she was unmarried, and her too-early pregnancy was a scandal to the whole village.  There would have been no corroboration of the miracle, no protection.  She would have been exposed to the contempt of her neighbors, and not only for the six months after her swollen belly became visible -- she would have had to eat derision and insult with her daily bread for as long as she lived.  As for the social effects on a young child: growing up with the shame of being called a bastard must be almost as painful as being illegitimate in fact." (19-20)
    Mitchell goes on to portray the effects of such charges of illegitimacy on the family, on the young child, and indeed on the beliefs and attitudes of the adult Jesus.  Yet there is at least as much reason to believe that the entire nativity story arose later and that in fact Jesus had a normal birth in a normal family and grew up normally.  Read on:
4)  Almost the only conclusions that can be drawn from the failure of Mark and John to report at all on Jesus' birth are
    a) that Jesus' birth was not of importance to them, and/or
    b) there was nothing remarkable about Jesus' birth. 
John P. Meier is inclined to discount Mitchell's view (above) that Jesus almost certainly grew up with the accusation of illegitimacy (regardless of the truth of such an accusation).  A likely scenario is that Jesus' birth (and family situation) was quite ordinary; that the infancy narrative was invented by the early church because founders of religions and rulers of empires were supposed to have divine origins; and that accounts of illegitimacy which became widespread in the second century among opponents of Christianity had already arisen by the time Matthew was writing -- perhaps in the early 80s.  It would appear that, in response to some of these early accusations, Matthew tried to cover his flanks in several directions: 1) by implying that sexual irregularity had good and respectable precedents, 2) by asserting that if Jesus' birth was irregular, it was because of divine intervention, and 3) even if there was no gossip of irregularity in Jesus' birth, as a divine ruler Jesus must have had a miraculous birth.
5)  In response to the villagers' question, "Is this not the son of Mary?", Meier (I.226) points out Old Testament precedent for such usage, in cases where the mother is more famous than the father, or (similarly) where the mother is widowed and the father perhaps no longer clearly remembered; he asserts that at Jesus' time this was not a way of referring to illegitimacy, though it became so later.  (See below, Matthew 13:53-58.)

SEXUAL IRREGULARITY AND ILLEGITIMACY
    Sounds like heresy, doesn't it?  Sexual irregularity and illegitimacy: Bad enough in the Bible in general, but in connection with the birth of Jesus? How could this be?
    Of course Matthew doesn't talk about such things directly.
    So where's the evidence?  Try this: If you read through Matthew's genealogy of Jesus, really paying attention, you saw mention of just four female ancestors. They are the clue.  Read on:
SOURCES
Genesis 38
Joshua 2
Ruth
2 Samuel 11-12
Mark 6:1-6