A "Christian" argument for antinatalism

https://randalrauser.com/2019/03/a-christian-argument-for-antinatalism/

To begin with, this isn't an original argument. Antinatalists have been using variations on that argument as a pressure point against Christians. 

Let's consider the first premise:

(1) The belief that there is a reasonable chance (e.g. more than 20%) that your future child would be born with a horrifying and untreatable disease like Stevens-Johnson syndrome would provide a good reason to avoid having children.

i) Really? That's hardly self-evident. That consideration must be counterbalanced by the good of having other children. To avoid having a child with Stevens-Johnson syndrome by avoiding procreation in toto deprives other future children of the opportunity to have a good life. So this is not a question that can be answered in isolation to what may be countervailing considerations. Acting for the sake of more than one party. Rauser oversimplifies the issue.

ii) In addition, this life is not all there is. This life is just a nanosecond in relation to everlasting life. So the real choice would be between the nonexistence of a child with Stevens-Johnson syndrome or the existence of a child who temporarily suffers from that disease, but may have the opportunity to enjoy eternal happiness. Suffering at the front end is the only way to find happiness at the back end. So, once more, Rauser oversimplifies the issue. 

Since Rauser isn't stupid, he's probably aware of the fact that his formulation is devious. He deliberately suppresses relevant factors. Moving along:

(3) Therefore, if the belief that there is a reasonable chance that your future child would be born with Stevens-Johnson syndrome would provide a good reason to avoid having children, then the belief that there is a reasonable chance that your future child would ultimately experience eternal conscious torment provides a good reason to avoid having children.

In addition to building on a false premise (see above), this seems to operate from the general principle that no one should be allowed to be happy unless everyone is happy. No one should go to heaven if anyone goes to hell. Better for no one to exist than for some to be happy if anyone is miserable. 

But why should we accept that principle? And it's not as if the happy group are happy at the expense of the miserable group. Rauser acts like the wicked should be able to deny everyone else a joyful existence. Why should the wicked by granted ultimate power over the fate of everyone else? What kind of perverted logic is Rauser appealing to?