Tradition
St. Irenaeus
Fragments from the Lost Writings of Irenaeus
Chapter 29
The Gospel according to Matthew was written to the Jews. For they laid particular stress upon the fact that Christ [should be] of the seed of David. Matthew also, who had a still greater desire [to establish this point], took particular pains to afford them convincing proof that Christ is of the seed of David; and therefore he commences with [an account of] His genealogy.
Source: Fragments from the Lost Writings of Irenaeus (New Advent)