The most widely accepted explanation is that
Matthew 1 traces Joseph's legal lineage (demonstrating Jesus's legal right to David's throne), while
Luke 3 traces Mary's biological lineage (demonstrating Jesus's blood descent from David)
[38]. This was common practice when inheritance rights were involved
[39]. Matthew uses 'begat' (legal succession), while Luke uses 'son of' (which can mean descendant or son-in-law)
[40]. The differences include: Matthew goes Abraham to Jesus (Jewish audience), Luke goes Adam to Jesus (Gentile audience)
[41]. Matthew emphasizes kingship through Solomon's line, Luke emphasizes priesthood through Nathan's line
[42]. Both lines converge at David, fulfilling the Messianic requirement
[43]. Additionally, levirate marriage laws could create situations where someone had both a biological and legal father, explaining some genealogical complexities
[44]. Both genealogies serve their authors' theological purposes while maintaining historical accuracy.