Hey there, thanks for responding. No, I'm not presupposing any metaethical commitments here. The argument is simple: If it's unjust to condemn an innocent person to death, it's unjust to procreate. Your idea of injustice could be culturally contextualised. That means it doesn't really matter how you think this is unjust, so long as you think it's unjust, the argument will follow.
This is irrelevant but it's worth considering. I think everyone of us do hold objective moral standards. No sane person will say killing for fun isn't wrong. Nor will anyone say genuine charity isn't good. Sure, there are some contentious things, but adopting relativistic standards for some actions doesn't negate objective moral standards.