If genealogy was so central to Jewish people, why did Mark omit it? Also, if Matthew and Luke were following the text of Mark, what made them mention the genealogy of Jesus?
Mark immediately draws attention in his book to two prophecies. He quotes Malachi first, despite that Isaiah is the greater prophet and despite that Isaiah is first in precedence in history Thus, Mark draws attention to Malachi's prophecy.
Mark draws attention to the messenger of preparation and to the messenger of the covenant, who is the Lord himself :
and the Lord, whom ye seek, shall suddenly come to his temple, even the messenger of the covenant, Malachi 3:1 KJV.
Thus, from the very first words of the book, Mark is setting forth the One who, being the Lord himself, is the only proper person to, himself, express the everlasting covenant, the New Testament.
This is also expressed in the epistle to the Hebrews which bears a number of similarities to the book of Mark. One of these similarities is the mention of Melchizedek, who has no genealogy, of whom the writer to the Hebrews states :
Without father, without mother, without descent, having neither beginning of days, nor end of life; but made like unto the Son of God; abideth a priest continually. Hebrews 7:3 KJV.
I think that this is the reason Mark begins his book at the place in Jesus' life that he does. Mark immediately (a word used oft in his book) presents John the Baptist, the voice crying in the wilderness, and then immediately presents the messenger of the covenant, the Lord himself.
Mark draws attention, as does the epistle to the Hebrews, to the Deity of the One who is sent to expound the New Covenant.
This is also, I would say, why Mark records the actual words that Jesus spoke on the cross 'Eloi, Eloi' in his own dialect - his own actual speech - rather than, as Matthew, record the Hebrew from which Jesus is quoting. Mark is drawing attention to the very utterance of the Lord, the messenger of the covenant, and drawing attention (as does the writer to the Hebrews) to the importance of the setting forth of the New Covenant.
The aspect of Jesus Christ, the Son of God, which Mark sets forth does not require an account of his genealogy. It would detract from the immediacy of the Person and the message to enter into a detail which others have, already, set forth in different aspects.
The content of each Gospel was determined by the intended audience of each.
Matthew wrote largely for a Jewish readership and so included numerous incidents to show that Jesus was the prophesied Messiah, the fulfilment of OT prophecies. Therefore Matthew includes a genealogy tracing Jesus back to Abraham, the Father of the Jews.
Luke wrote largely for a Greek readership and included numerous incidents about non-Jewish people, centurion and the Perean ministry. Thus, Luke included a genealogy tracing Jesus back to Adam, the father of all mankind.
Mark wrote largely for a Latin readership and selected his incidents accordingly. It is therefore, the briefest of the Gospels and has no need of genealogies on which the Latins we much less interested.
Therefore, while the synoptic Gospels share many similarities and some passages that almost verbatim, they also show some independence from each other in their selection and wording of incidents to suit their readerships.