Late last month, the Mississippi Supreme Court heard oral arguments in a case about the rights of female same-sex couples that shows that we have a long way to go to achieve true and complete marriage equality. The case, Strickland v. Day, is about whether to have the non-birth parent listed on a child’s birth certificate when an anonymous sperm donor was used. It’s also about whether the spouse that does not bear a child conceived via artificial insemination has a right to be treated as the full legal parent of that child.

If some of this sounds familiar, it is because it has already played out in a similar fashion in Arkansas earlier this year. In Pavan v. Smith, the U.S. Supreme Court considered whether Arkansas was violating the Constitution when it refused to let married female same-sex couples list both parents on the child’s birth certificate. At the time, Arkansas law mandated that in cases of artificial insemination involving opposite-sex couples, the male spouse’s name was required to appear on the birth certificate regardless of the fact that he had no biological relationship to the child. Arkansas decided, however, that it wouldn’t extend that same right to the female spouse of a woman who had conceived a child during the marriage by artificial insemination.

In June 2017, without even holding briefing or an oral argument, the Supreme Court agreed with the two female same-sex couples who had filed lawsuits. It found that the decision affirming marriage equality, Obergefell v. Hodges, was meant to cover ancillary marriage rights, including proper representation on birth certificates. However, Chief Justice John Roberts and Justices Neil Gorsuch, Clarence Thomas, and Samuel Alito wrote a dissent, saying the Court should have fully considered the case. In so doing, Gorsuch signaled his hostility to a broad view of rights for same-sex married couples.

Several months after the ruling, Arkansas persisted in refusing to issue birth certificates to female same-sex couples reflecting both names. Indeed, for a brief time, it didn’t issue issue any birth certificates at all following a lower court judge’s injunction forcing the state and the same-sex couples to come to agreement on language to be struck from the law in question. Finally, earlier this month, Arkansas’ governor ordered the state to start doing so.

At roughly the same time as the Arkansas case, the Mississippi case had begun making its way through the state courts there.

It began, as these things sometimes do, with a divorce that was complicated by the fact that marriage equality was not the law nationwide until just recently. Kimberly Day and Christina Strickland are Mississippi residents who were initially married in 2009 in Massachusetts. Day conceived and bore a child in 2011. Of course, at that time, Mississippi did not recognize their marriage, and therefore would not have recognized Strickland’s parentage in any event. Because of that, Day’s name was listed on the birth certificate, but Strickland’s was not. When they divorced in 2016, marriage equality was the law in Mississippi, but Strickland’s absence from the birth certificate left the couple’s child, Z., in limbo.

In the decree granting the divorce, the family court judge wrote at length about his problems with treating both parents as co-equal in terms of the custody of Z.  And, unsurprisingly, his argument revolved around a very limited (and, in the post-Obergefell era, untenable) view of the rights of same-sex couples. First, he fixated on the donor:

Z has got a natural father somewhere. Our Supreme Court has been very, very strict about parental rights and absent fathers. And there is a natural father somewhere of Z, whose parental rights have not been terminated.

He then fixated on the conception itself, stating that since two women can’t conceive a child together, Z. was a child born during the marriage, but not of the marriage. Therefore, he denied Strickland any custody rights, instead granting Day the complete legal and physical custody she requested. By doing so, he also, perhaps accidentally, created a situation where the anonymous donor would have both the rights and responsibilities of parentage until their rights were explicitly terminated—which is likely a thing most anonymous donors did not bargain for.

Strickland appealed, and the case is now before the Mississippi Supreme Court. She pointed out that in this instance, the donor was anonymous and unknowable, she and Day had signed express consent acknowledging they were both the parents of the child prior to the insemination, and Day, the birth mother, agreed she would never seek the identity of the donor. She also noted the near-impossibility of finding an anonymous donor in order to terminate parental rights.

Most notably, what Strickland’s argument rests upon is that Mississippi already has laws about marital presumption—the idea that a child born into a marriage has a parent-child relationship with both spouses, even if those children were conceived via any sort of assisted reproductive technology. Also, like Arkansas, Mississippi law requires the “the name of the husband shall be entered on the certificate of birth as the father of the child” if the mother is married at conception or birth. Further, Obergefell compels states not only to recognize same-sex marriage but all the ancillary benefits of marriage. And although Pavan was decided after this custody fight had started, the Supreme Court ruling there compels states to specifically add a female spouse to the birth certificate when the child was conceived via artificial insemination during the marriage. With those things in mind, the lower court’s decision denying Strickland parental rights—and Day’s attempts to preserve that decision—should not stand.

At oral arguments before the Mississippi Supreme Court, Day’s attorney argued that Strickland would have full parental rights had she only tried to find the sperm donor to give him the chance to agree to terminate his. This, of course, ignores that (a) the donor is anonymous and known only by a number; (b) Day signed an agreement saying she’d never try to find or identify the donor.

Day may view this as a narrow attempt to preserve her full custody rights, but a victory for her could have significant negative implications for married couples who conceive via artificial means. If this ruling were limited to female same-sex couples, it would run afoul of Obergefell, and create major difficulties that must be overcome in order to be listed on the birth certificate. Alternatively, the Mississippi Supreme Court could decide that all couples who use assisted reproductive technology should be saddled with the burden of attempting to hunt down anonymous donors and terminate parental rights.

And if spouses can’t automatically appear on a child’s birth certificate when assisted reproductive technology is used, this has major implications for custody battles and ongoing parental rights. A spouse who is not listed on the birth certificate, for example, as no automatic legal right to joint custody of a child after divorce.

Regardless of outcome, the mere existence of this case makes clear that same-sex couples are going to have to fight tooth and nail, state by state, court by court, in order to obtain all the benefits, rights, and responsibilities of marriage.