1 Corinthians 7:13

And the woman which hath an husband that believeth not, and if he be pleased to dwell with her, let her not leave him (KJV)

Then: Paul continues to discuss mixed marriages. He follows the same pattern of this section. Concentrating on a specific aspect of his concern, he alternates between addressing the man and the woman, sometimes one first and sometimes the other (Baker, p. 98). The approach emphasizes his teaching of mutual submission. The Holy Spirit indwells all followers of the Lord never giving greater value to anyone. This accords with the teaching of Peter whose words are recorded in Acts 10:34-35, "Of a truth I perceive that God is no respecter of persons: but in every nation he that feareth him and worketh righteousness, is acceptable to him."

Now: Paul continually honors the hope of living a life of following Christ. He understands and promotes the belief that it is both easier and better to concern oneself with spreading the gospel to others rather than put the concerns of a spouse above ministry. Accordingly, his follow-on discussion of the effect on the whole family points to the spiritual, not the practical effects of family/societal disruption of single parent families.

Extra source: Cornerstone Biblical Commentary 1 Corinthians (William Baker), 2 Corinthians (Ralph Martin & Carl Toney), ed. by Philip Comfort. Carol Stream: Tyndale House Publishers, c2006.