A person's family tree is pretty important when it comes to verifying who someone is. There are however two main problems with the family tree(s) of Jesus Christ.

Contradicting Trees

A more straightforward problem is that the family tree in Matthew does not match up with the one in Luke. They both give a detailed family linage from David down to Jesus but the only places they agree upon are that of Salathiel being the father of Zorobabel and that of Eliakim fitting somewhere between David and Joseph. The rest of the order is completely different, none of the other names even appear on the other's list and the account of how many generations from David to Joseph in Matthew is almost half of what Luke claims. The book cannot even agree on who Jesus' Grandfather was.

Mary's bloodline?

Is the second account in Luke actually Jesus' bloodline through Mary? There is no mentioning of this in the Bible and if this was true then both Joseph & Mary would have been 10th generation cousins. It is very unlikely that after David the family tree split off then rejoined again with Salathiel and Zorobabel then split off again only to reunite again with Joseph and Mary. This would also mean that Mary's side of the family would have to steadily reproduce almost twice as fast as Joseph's side to explain for the double size of generations. Historically there is absolutely no reason why Luke, or anyone, would have listed the family tree of husbands of the mothers on Mary's side of the family.

The claim that Luke is Mary's family tree is something preached by Christian apologists in an attempt to cover up the obvious contradictions. Such a claim is not supported by the Bible nor any historical knowledge. Luke's genealogy was not labeled as Mary's until as late as the 15th century CE, when Annius of Viterbo first suggested this reassignment of the genealogy to Mary. Matthew and Luke disagree on a lot in the Bible, this is just another example.