Why would Abraham ask Sarah to say she was his sister?

Why would Abraham ask Sarah to say she was his sister (Genesis 12:13; 20:2)?

Abraham’s response was driven by his fear of being killed by men who would long for his beautiful wife. It was understandable enough that Sarah complied with his request under those circumstances. Yet it was a sin on the part of both of them, and it robbed them of all possibility of witnessing to the truth of God before the idolatrous society of Egypt.

It seems quite clear that this account of Abraham’s failure is an honest inclusion of his lack of faith as manifested by this entire episode. If he had not believed that Yahweh was able to protect him with honor and integrity if he went down to Egypt, then he should never have gone there at all. As it was, he brought dishonor on himself and the cause he stood for, discrediting himself before the moral standards of Egypt itself.

–Encyclopedia of Bible Difficulties