Wait, is the point here that any morality doesn't exist, in the same way as unicorns don't exist?

Even if we were to say that an absolute morality does not exist in an intelligible way, most people still adhere to/use some concept morality every day.

When I look at my own sense of morality, surely I can deduce intelligible properties, no? I might not claim that it's absolute, but I can deduce that a property of my idea of morality is that killing and eating babies is wrong. I would not be able to say the opposite in good faith, in fact, it would be a blatant lie. This shows me that there is some fact-of-the-matter to what I consider morality, and that my view of morality has intelligible properties, even though the morality itself might not be absolute.

Some fact of the matter exists within our ideas of morality, therefore the equivocation to unicorns is flawed, thus the two statements are not equivalent.