What is the necessity that permits acting upon the fatwa allowing the breastfeeding of an adult to make the orphaned girl—who is 12 years old, lives in the home, and whose affairs the questioner oversees due to his guardianship—a mahram to him and his wife, especially given that his wife is currently breastfeeding?

A girl who has reached puberty or is close to it is considered to be like adult women. Therefore, she must be treated on this basis. It is not permissible to be alone with her, or for her to uncover her hijab (definition) in your presence, and other such actions that are not permissible with a non-mahram (definition). The preponderant opinion is that adult suckling does not establish a prohibited degree of relationship, contrary to those who permitted it out of necessity.