XX/XY is not the only system of sex determination. The system @milla101 was referencing is the XX/X0 system, where females are XX and males are X0, meaning they have one X chromosome. (This isn’t the system in mice, though – they’re XX/XY, I believe the only known XX/X0 species are insects – grasshoppers, for example, are XX/X0.) I have no idea whether the XX/X0 system could somehow evolve from the XX/XY system, as I haven’t studied the genetic underpinnings of this, but it seems unlikely.
As of now, humans with only one X chromosome appear female, and have what is called Turner Syndrome. They’re infertile and have a few other problems that have to do with gene dosage (not having enough of what’s encoded on the X chromosome). This also proves that there are still some important genes on the Y chromosome. :)