If "reproduction" were an organism replicating and making a copy of itself, how is a child/offspring not a mere extension of the "parent(s)"? In humans, the human child/offspring inherits 50% of their DNA from each "parent". Why wouldn't that mean that the child/offspring is a mere mixture of both "parents"? That the child/offspring is the "parents" continuing on in the body of the child/offspring? Of course this conclusion would have disastrous and catastrophic outcomes. It'd mean that the "parents" could do anything to the child/offspring and it wouldn't be "abuse". It would, at worst, be "self-harm" as the "parents" would be "harming" a part of themselves. Not someone else. My question is to understand why the child/offspring is not the "parent(s)"? What makes the child/offspring different from the "parent(s)" when the DNA of the child/offspring, what makes the child/offspring what they are, comes from the "parent(s)"?
Reproduction is not considered to be "an organism making a copy of itself" for any organism but very primitive species who can reproduce by fission like bacteria or worms. Whether a worm cut in half becomes two individual worms or the original worm plus its extension is left for anyone to decide.
Sexual reproduction yields an individual with its own DNA, albeit it comes from mixing the DNA of both of its parents the new set of combination is entirely original.
Also you seem to reduce identity to DNA, a position even the most radical of physicalists would not hold: think about homozygote twins, they share the exact same DNA and yet they can grow up to be very differently minded individual, and nobody in their right mind would consider them to be emanations of the same individual or extensions of one another.
The reason is that, along with DNA, what defines us is our memory (whether conscious or subconscious), who informs all of our moods, decisions and judgements. Wether this memory is physical or immaterial is irrelevant. Consider people with the same DNA but raised appart in different countries, classes, religious group. Although they share some likeness and predispositions, they won't grow up to be the same person and might very well hate each other's guts (for example if onw twin was to be raised by protestants and the other by catholics in XVI century Europe).
Aside from that we all grow up with a sense of self that very soon differentiate us from our parents: we don't feel what they feel, they can be harmed without us being harmed, and vice versa, they die and we continue living. I don't think you would approve of your parents now deciding to terminate your life because it would just be "self harming" on their part. You perfectly understand how it would harm you, because you are your own individual. We all share this conception, and that's why it is not considered acceptable for parents to decide of their children's fate in most places (and even in places where it is, it's more because children are considered property of their caregivers, not extensions).