Lyric discussion by wolfcreature 

Cover art for Genesis 30:3 lyrics by Mountain Goats, The

I interpret this song as from the perspective of Abraham, speaking to his wife Sarah.

The bible verse in the title (Genesis 30:3) depicts Sarah (who believes herself to be barren) telling Abraham to impregnate her handmaid Bilhah so that the married couple may have children "through [Bilhah]."

When God eventually grants Sarah a child by Abraham and she becomes pregnant with Isaac, she becomes extremely hostile towards Bilhah. Worried about Isaac's inheritance as second son, Sarah demands Abraham cast out his first son Ishmael and the child's mother Bilhah. Abraham obliges.

This story speaks to the 4th verse of the song, where the narrator sees his child's face only once before it's "gone forever." The tale also explains the repeated somber refrain of "I will do what you ask me to do because of how I feel about you," as though Abraham were speaking directly to Sarah.