The New Testament gives Jesus' genealogy ending with Joseph but Joseph was not his biological father. He was conceived by the Holy Ghost. Mary was his biological mother, so why wasn't she mentioned?
One possible response to your question is that the genealogy in Luke is actually the genealogy of Mary. Some Reformed scholars have held to this interpretation. For example, William Hendriksen says, "It is not true that the genealogy presented in Luke 3:23-38 is necessarily that of Joseph. On the contrary, it is probably that of Mary" (Commentary on Luke, p. 225). The same view was held by J. Norval Geldenhuys ("That Matthew gives the family tree of Joseph and Luke that of Mary also fits in beautifully with the contents of the first chapters of their Gospels," NICNT Commentary on Luke, p. 152).
In fact, the view that Luke's genealogy is of Mary is perhaps the most popular view among evangelicals in general. "Matthew 1:1-16 gives the genealogy of Jesus through Joseph.... Luke 3:23-38, on the other hand, seems to record the genealogical line of Mary herself..." (Gleason L. Archer, Encyclopedia of Bible Difficulties, p. 316). "[in the two genealogies we have] two different lines of ancestors, one traced through His legal father, Joseph, and the other though His actual mother, Mary" (Norman Geisler and Thomas Howe, When Critics Ask: A Popular Handbook on Bible Difficulties, p. 385).
My own opinion, however, is that both genealogies trace Jesus' birth through Joseph. That view is very ably expounded and defended in Chapter VIII of J. Gresham Machen's The Virgin Birth of Christ and is favored by many modern New Testament scholars as well.
Matthew's account focuses on Jesus' claim to be the Son of David. This is also true of Luke's account. Matthew mentions Mary ("the husband of Mary, of whom Jesus was born"). Luke does not, by name, though Luke 3:23 does imply the virgin birth ("Jesus ... being the son [as was supposed] of Joseph"). Such indirection strongly suggests the other-than-human origin of Jesus. And, interestingly, the beginning and end of Matthew's genealogy record 'miracle' conceptions (Sarah and Mary).
The question is, why the prominence given to Joseph? He was the representative of David's line, hence Joseph was Jesus' legal rather than his biological father. God purposed to preserve David's line because of his plan to send his Son Jesus to be the Redeemer. Because Joseph was Mary's husband, Jewish law regarded Jesus as his son. In other words, it was God who "implanted" Jesus in David's line. This was not by way of an act of Joseph, but of God.
These two genealogies present difficulties, but to face these difficulties is for another time!
I hope I have shed some light on this subject. Thank you for writing.
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