I don’t know why testing isn’t the first thing someone would suggest.
Reading the comments to the story on Reddit, I saw that he is sterile and can't have children due to an injury before they were married. It may not have seemed so bad to her when they were 21 and got married, but possibly she began to feel that her life will be incomplete without children; so first she "fixed it" unconsciously, and now wants to "fix it" some more, but it's all falling apart.
Great immaturity. Sad, sad situation for the child.
Still, other posters are correct that the law in many states says that any child born during the marriage, biologically related to the father or not, is legally a child of the marriage and the legal responsibility of the man. Don't know which state he is in, tho.