If it is unjust to condemn an innocent person to death, then it is
unjust to procreate.
Here is a simple argument you can use:
The argument "if it is X to Y, then it is X to Z" relies on a similarity between Y and Z, and a meaningful definition of X that applies to both Y and Z.
The article does not establish a similarity between "condemn an innocent person to death" and "procreate". Because the similarity is unsubstantiated, the argument is illogical. The conclusion that it is unjust to procreate doesn't follow from any of the arguments presented.
The article uses a meaningless definition of "injustice", which makes both the antecedent and the consequent ungrounded, and therefore the argument is illogical (it would still be illogical if even just one of them were ungrounded).
Let's take a closer look at #1:
To condemn something to death, the something must exist. If it doesn't exist, you cannot interact with it at all. If you use a loose definition of "condemn" meaning making a judgement about, or a negative statement about something, then it's possible to condemn all sorts of imaginary things. But if something is imaginary then condemning it to death is meaningless. Therefore, for this argument, the thing needs to exist and be alive.
To procreate is to produce new creatures that are alive.
These things are not similar. The parts of the article trying to argue that they are similar fail badly. The article starts with a story about a prisoner with a death sentence who doesn't remember committing the crime, and then makes all of that irrelevant by stating the prisoner was framed. Then, it makes the outrageous suggestion that "this is life".
You only need one contrary example to refute the claim that life is like being a framed prisoner with amnesia and a death sentence. You could do a survey of actual prisoners, you could reflect on your own life, or look around.
Whatever harm or suffering happens to a person is only an injustice if it was caused by other people doing something wrong or unfair. Procreating in general is not wrong or unfair. Only particular circumstances could make it wrong or unfair, and then the issue is with the circumstances, not with the act itself. Therefore, it's not similar to condemning an innocent person to death, and it's not even similar to condemning a guilty person to death. It's just not similar at all.
Let's take a closer look at #2:
Injustice is something unfair or wrong done to someone, so by definition it is a harm. It is obviously an injustice to condemn an innocent person to any sentence. But the author writes this:
It is morally wrong to take unjust actions (whether it inflicts harm
or not).
The author's formulation here is like saying, "you are wet (whether you are covered in liquid or not)". It makes the word "wet" meaningless in that context.
The use of a meaningless term in this way makes the argument ungrounded, because you can't evaluate the result of its application to anything.
According to the author's definition, an injustice could inflict harm or not inflict harm. That's not the same definition most people would use. With this definition, why would it be morally wrong to do injustice? If harm isn't a requirement, couldn't anything be an injustice?
The author writes:
Importantly, a state of affairs can be unjust even though it inflicts
no harm to anyone. An example of this is arbitrary favoritism, whereby
one group of people receives benefits while another doesn’t.
The author's assertion is incorrect. Not all harm is an injustice, but all injustice involves harm. Fairness is decided by the consensus of people with legitimate claims, and there is a multitude of ways of doing things that are generally considered fair and thus easily gain consensus. Unfairness harms people by depriving them of a resource or benefit they had a legitimate claim to receive. Favoritism is an obviously unfair system of distributing limited resources or benefits, and something unfair done to someone else is in the definition of injustice.
Even if we pretend for a moment that there exists a kind of injustice that does no harm, we immediately have a new problem: In what way other than causing harm is it an injustice to condemn an innocent person to death? In what way other than causing harm is it an injustice to procreate? The author makes no attempt at defining this.
Conclusion
The author tries to mislead you with what appears to be an obviously true antecedent "it is unjust to condemn an innocent person to death", but is actually ungrounded because the word "unjust" in this context has been redefined by the author to be meaningless.
Without a meaningful definition of what "injustice" means in this context, you can't evaluate whether a statement "it is unjust to X" is true or not.
The consequent is similarly ungrounded.
Even when using the regular definition of injustice, there is no similarity between the two things being compared because one of them causes harm to an innocent person while the other one creates an innocent person.