Q. Why does Abraham call his wife his sister (Gen. 12:13, 20:2)?A. It was a form of self-protection. He was afraid that if he told outsiders that she was his wife, they would do anything including killing him in order to take her (Gen. 12:11-13).
The first time the problem arose he asked her permission to call her his sister, though the Torah does not record her agreement; the second time she apparently said he was her brother (Gen. 20:5). He seems to have called her his sister wherever he went (Gen. 20:13).
He was castigated by the sages for putting her honour at risk and when the deception was discovered it was he, not she, who was blamed (Nachmanides).
In an attempt at self-justification, Abraham stated, “She is indeed my sister, the daughter of my father but not the daughter of my mother, and so she became my wife” (Gen. 20:12).
Whilst even this was prohibited by the Torah, it was permitted according to the Seven Noachide Laws applying to all mankind before Sinai and to non-Israelites thereafter (Rashi on Gen. 1:30).
True, there is a common belief that the patriarchs kept the whole Torah before it was given, but not all the sages accepted this view.
Abraham’s claim that Sarah was his half-sister was not literally true, according to a rabbinic tradition recorded by Rashi (commentary on Gen. 20:12), who argues that she was really his niece, his brother’s daughter, but since grandchildren are considered one’s children, she was regarded as Terach’s child and therefore metaphorically Abraham’s “sister”.