Let me go; why should I kill thee? - That is, If thou do not let me go, I will kill thee. This she said to excuse herself to her father: as a wife she could do not less than favor the escape of her husband, being perfectly satisfied that there was no guilt in him. It is supposed that it was on this occasion that David wrote the fifty-ninth Psalm, Deliver me from mine enemies, etc.
Why should I kill thee? - To avert Saul‘s anger from herself, she pretended that David had threatened her life unless she facilitated his escape.