Anyway, it's quite easy to justify. Raising children necessarily involves an innocent, non-consenting third party, and so cannot possibly be treated as a right. Assuming you're okay with the government taking kids away from abusive parents after the fact, I'm not sure why you wouldn't want the government to prevent people who have abused kids in the past from abusing more kids.
The "natural human instinct" (not that I consider that criteria relevant to anything) part is having sex, which I would not stop people, even relatives, from doing assuming everybody involved is consenting. Thankfully it is quite possible to have sex without procreation, and since I believe in abortion to a point it doesn't matter to me if the birth control fails.
I'd certainly draw the line no earlier than those who have clearly demonstrated they are a risk to children, or cannot take care of children (e.g. severely mentally challenged). While it's true that we ought to be conservative in how we apply it, I just don't buy into the slippery slope argument of it being inevitably abused.