John Lightfoot on Matthew 1:16

[And Jacob begat Joseph the husband of Mary.] The mother's family is not to be called a family. Hence the reason may very easily be given, why Matthew brings down the generation to Joseph, Mary's husband; but Luke to Eli, Mary's father. These two frame the genealogy two ways, according to the double notion of the promise of Christ. For he is promised, as the 'seed of the woman,' and as the 'Son of David'; that, as a man, this, as a king. It was therefore needful, in setting down his genealogy, that satisfaction should be given concerning both. Therefore Luke declareth him the promised seed of the woman, deducing his mother's stock, from whence man was born, from Adam; Matthew exhibits his royal original, deriving his pedigree along through the royal family of David to Joseph, his (reputed) father.