Sorry, Narkissos, but I can't see the circular reasoning. I checked this verse in several translations, and then in the original Greek (of which I don't admit to being any kind of scholar). The most literal rendering seems to be:
"For the unbelieving husband has been sanctified by the wife, and the unbelieving wife has been sanctified by the brother; since then the children of you are unclean, but now they are holy."
All translations use the word "otherwise" to connect the phrases, which says to me that the children are holy BECAUSE the unbelieving spouse is sanctified because the partner is a believer, that is, the status of the children is based on the status of the parents, not the other way around.
Also, in a practical application, I see at least four possible situations that would evoke concern:
1. Children born when both parents were unbelievers, and subsequently one became a believer,
2. One of the natural parents has died, and the believer has remarried an unbeliever,
3. One spouse became a believer and then children were subsequently born,
4. One spouse became a believer with no children yet born, but are anticipated.
So, does it apply to children already alive--are they "set apart" when at least one of the parents becomes a believer? And up to what age does this apply? One or more of these situations may have applied to an individual family. All of these issues would have been relevant.
(In denominations that practice infant baptism, isn't a special dispensation imputed to the child based on at least one parent's profession of faith until they reach an age of accountability? Could this passage be the basis for that doctrine?)
This issue may have arisen out of a concern by believers for the status of their children in the eyes of God, considering the other parent was not a believer. It would have been inconsistent with Paul's teaching that a person could marry into the faith (as some in the article have suggested). I don't know what the earliest church teaching was in regard to the spiritual status for infants and small children, but consider the relatively high mortality rate for children back then.