Your "all marriage laws are gender neutral" argument fails.
Lawriter - ORC
Chapter 3101: MARRIAGE
3101.01 Persons who may be joined in marriage - minor to obtain consent.
(A) Male persons of the age of eighteen years, and female persons of the age of sixteen years, not nearer of kin than second cousins, and not having a husband or wife living, may be joined in marriage. A marriage may only be entered into by one man and one woman. A minor shall first obtain the consent of the minor's parents, surviving parent, parent who is designated the residential parent and legal custodian of the minor by a court of competent jurisdiction, guardian, or any one of the following who has been awarded permanent custody of the minor by a court exercising juvenile jurisdiction: