Why does Joseph have two different fathers listed in Matthew 1:16 and Luke 3:23?

Notice Luke says as was supposed, while Matthew says begot. This is because Matthew records Joseph's blood relatives, while Luke records his adoptive relatives. For in Bible times if a man who was married died and had not any children, then they were obligated to marry their deceased brother's wife to have children raised in the name of the deceased brother. So they would be considered legally the deceased brother's child but actually a blood son of the brother who had children for him.