John Calvin Commentary Genesis 20:12

"And moreover she is indeed my sister, the daughter of my father, but not the daughter of my mother; and she became my wife:" — Genesis 20:12 (ASV)

And yet indeed she is my sister. Some suppose Sarah was Abraham’s own sister, though not by the same mother but born from a second wife. However, since the name "sister" has a wider meaning among the Hebrews, I willingly adopt a different conjecture: namely, that she was his sister in the second degree. Thus, it will be true that they had a common father—that is, a grandfather—from whom they had descended through brothers.

Moreover, Abraham extenuates his offense and draws a distinction between his silence and a direct falsehood. Certainly, he truthfully professed that he was Sarah's brother. Indeed, it appears that in his words he feigned nothing that differed from the facts themselves. Yet, when all things are sifted, his defense proves to be either frivolous or, at least, too feeble.

For since he had purposely used the name "sister" as a pretext to prevent men from suspecting his marriage, he sophistically gave them an opportunity to fall into error. Therefore, although he did not lie in his words, yet concerning the actual situation, his dissimulation was, by implication, a lie.

However, he had no other intention than to declare that he had not dealt fraudulently with Abimelech, but that, in a matter of great anxiety, he had seized upon an indirect method of escaping death, by the pretext of his prior relationship with his wife.