Valve haven't made Half-Life 3 yet because their attempts weren't good enough
Half-Life: Alyx is out today and, as you’d hoped, it is good. Graham-certified good, in RPS’s Half-Life Alyx review. For all its goodness, Alyx is not officially Half-Life 3, which Valve still have not made. There are a few primary reasons that the fabled “3” hasn’t made an appearance, Valve have now explained. Chief among them, they just weren’t happy with what they came up with.