This teaches that whoever brings up an orphan in his home is regarded, according to Scripture, as though the child had been born to him. A similar passage occurs in the midrash, where the question arises about what Hebrew name to use for a woman raised by a foster father. However, adoption as practiced in our modern society means the removal of all rights and responsibilities of the biological parent, and their transfer to another couple or individual. For all intents and purposes, the child's biological lineage is broken. This procedure has its roots in ancient Roman law, where the concern was finding an heir for a childless couple.
Jewish law is far closer to British common law than to ancient Roman law.
In Judaism, personal status is based on bloodlines and lineage, the moment of birth gives a Jew his or her identity. No legal procedure or court decree can erase that identity. This emphasis on bloodlines has serious consequences for adoption in Jewish law. For example, the status of the birth mother as Jew or gentile at the moment of birth establishes the identity of the child as Jewish or gentile. If the mother is Jewish, then the father's tribal status as a Kohen, Levi, or Yisrael decides the child's tribe.