The Supreme Court heard oral arguments in the Hobby Lobby and Conestoga Wood cases Tuesday, in which two companies have challenged the Affordable Care Act’s requirement that contraception be included in insurance plans. It’s a high stakes battle, in part because of Obamacare, but in part because of a much wider “religious liberty” movement that is attempting to carve out religious exemptions to civil rights laws. Hobby Lobby is the slightly less obvious cousin of Arizona’s “Turn the Gays Away” bill: same logic, same proponents, and same potentially devastating effects.

Reading the tea leaves of oral arguments is a fool’s errand. Perhaps a justice is needling an attorney because the lawyer’s argument is stupid. Or perhaps the justice is kicking the tires of an argument she wants to advance. From the outside, the behavior looks the same, and can lead to some amusingly wrong conclusions.

Still, advocates of reproductive freedom and LGBT rights have reason to worry. If today’s arguments were any indication, the odds appear stacked against them.

The most depressing aspect of the arguments was how everyone seemed to be playing to type. In a case about contraception, there was not a single female (or non-white) lawyer at the council’s bench. The strongest objectors to Hobby Lobby were the three female justices: Ruth Bader Ginsberg, Elena Kagan, and Sonia Sotomayor. Justice Scalia dismissed arguments he didn’t like with contempt. Justice Thomas stared silently at the ceiling.

Most likely, the decision is going to come down to Justice Kennedy, who, again playing to type, offered tantalizing clues to both sides. But at the end of the day, he seemed to side with Scalia, Thomas, Alito, and Roberts—and with Hobby Lobby.

Legally, the case turns on three questions. First, whether corporations are “persons” for the purpose of the Religious Freedom Restoration Act (RFRA), which protects the exercise of religion in all but extreme cases; the government argued that they are not, but its case appeared to collapse at the end. Second, if RFRA protects businesses like Hobby Lobby, whether Hobby Lobby’s religious practice (whatever that means) is “substantially burdened” by having to include contraception in its insurance plan. And finally, if there is a burden, whether the government can justify it with a “compelling state interest” and the “least restrictive means” of reaching it.

It seemed to me that Hobby Lobby went 3 for 3 and then some.

The arguments began with the liberal justices peppering Hobby Lobby’s lawyers with slippery-slope hypotheticals. If Hobby Lobby can deny coverage for contraception, why couldn’t a Christian-Scientist-owned company deny health insurance completely? What if a Muslim-owned company wanted to make employees were burqas on the job? What then?

Paul Clement, Hobby Lobby’s lawyer, appeared to whiff on this one. He said, well, those cases are different, and would be litigated case-by-case. This is hardly conservative jurisprudence: leaving a mess of uncertainty, followed by a mess of lawsuits. And yet, when the conservative justices spoke, they seemed unworried. If there was to be a flood of litigation, we’d have drowned in it by now. Actually, there aren’t that many Hobby Lobbies out there.

So what about this idea that not only are corporations people, but people with consciences?

Here, the justices seemed to focus on legalism. The weirdness of a corporation practicing religion featured less in the argument than whether Congress meant to include corporations in RFRA’s definition of “persons.” Other laws, such as the aptly named Dictionary Act, expressly do so. And even though RFRA isn’t explicit, the conservative justices seemed persuaded that it should be read similarly.

The worst moment, on this front, came right at the end of Solicitor General Donald Verrilli’s argument. Justices Kennedy and Alito kept after him, demanding that he clarify his position on whether corporations are “people” or not. General Verrilli tried to weasel out of it. Finally, Justice Kennedy said to him, “Your reasoning would allow corporations to be forced to pay for abortions.” The chamber was silent. Verrilli had to say “Well, even if you disagree with me on this question….”

In other words, D’oh.

Now, in the abstract, it’s not clear what would be so awful about a corporation—not an individual, but a business—being “forced” to pay for abortion. In actuality, it’s not realistic, and that’s probably a good thing. But the whole point of corporations being “people” is that they are distinct from their owners, officers, and employees. So even if Hobby Lobby’s owners consider abortion to be murder, the sins of the business are not the sins of the boss.

But if you know Justice Kennedy, you know that his remark was basically rhetorical. It’ll be a cold day in hell before Justice Kennedy allows anyone to force a corporation to pay for an abortion. Which is why Verrilli caved—and why the “corporations aren’t really people” argument, despite its common-sense appeal, seemed to be dead in the water.

That left the two remaining prongs of the RFRA investigation: whether there’s a “substantial burden” on the company, and if so, whether there’s a compelling state interest and least-restrictive remedy to justify it.

Early on, Justice Kennedy seemed to offer hope to the pro-choice side. Noting that Hobby Lobby could simply not provide any insurance at all, and simply pay a $2,000-per-employee annual tax, he asked “how is the employer hurt?” When Clement (and the conservative justices) tried to throw in extra costs (e.g. for increasing salaries to compensate for not offering health benefits), Kennedy persisted. “Say it’s a wash. What is your case?”

Clement wasn’t left with much—only an even weirder claim that Hobby Lobby considers it a positive religious obligation to provide health benefits. In other words, Hobby Lobby must be allowed to provide some insurance, but may not be forced to provide some other insurance.

Of all the legal arguments made in court, this seems on reflection to be the government’s only hope. And yet, it rests on a weak foundation: that not offering health insurance, and most likely losing competitive advantage as a result, isn’t a substantial burden. Justice Kagan, in particular, effectively said “so what?” But is that really true? Is it really a trivial thing to not offer a desired benefit to employees? I guess we’ll see in June.

The government (as well as advocates for women, LGBT people, and secularists) fared the worst on the compelling state interest/least restrictive means issue. Justices Roberts and Kennedy argued that if the compelling state interest in women’s health (no one mentioned freedom here) is so strong, then what about the many governmental exemptions that already exist, from grandfather clauses to religious exemptions for nonprofits? As for least restrictive means, the conservative justices seemed to agree with Hobby Lobby that a better solution would be for the government itself to pay for the contraceptive coverage. Women would get their health care, Hobby Lobby’s owners would rest easy, and we could all move on.

Ironically, that last point collides with another religious liberty case, in which the Catholic order “Little Sisters of the Poor” (can you imagine a more sympathetic plaintiff?) is arguing that even filling out an exemption form is a “substantial burden” since it enables someone else to provide contraception. Clement had to tiptoe around that argument, since it would torpedo his proposed solution to the Hobby Lobby quandary, even as his allies are arguing it elsewhere. But, court watchers, take note: even Justice Alito didn’t seem impressed by it. I wouldn’t bet on the Little Sisters.

What’s strange about Hobby Lobby is that it seems intuitively like an easy win for progressives. Of course companies can’t pick and choose which laws to obey. Of course they don’t have consciences, even if their owners do. And of course they can’t discriminate against women.

Yet the letter of the law seemed to cut the other way today. If the court can limit the slippery slope—maybe this is just about contraception, or just about Obamacare, or just about closely-held corporations—the 6,000 women who work for Hobby Lobby may have to pay for their IUDs, even as the 14,000 male employees get Viagra, and even penis pumps, covered.

At the end of the day, though, there’s a chance that that inequity may yet be dispositive. As Justice Kennedy noted, “this creates a disadvantageous position for some employees.” One can only hope that the overwhelmingly white, overwhelmingly male population in the courtroom can appreciate that.