There is no such thing as a perfect copy. That's what the OP is about! Even if there were some sort of magical philosophy box that made perfect replicas, you would cease to be perfect copies of each other as soon as you exited the box and started receiving different percepts - you would become different physical sentient entities leading separate lives. If you want to believe that these two clones are in fact the same identity, then you have to provide a specific reason - for example: related histories, similarity of behavior, motivation & drives, etc. Furthermore it would have to be a fuzzy comparison because as soon as you exit the box you start to diverge. How much change does it take until you can no longer claim that you and your clone are the same person? A week? A year? One hundred years? At that point you and your clone will have lived move time separately than your shared history. Do you still have the right to claim the other as a direct extension of yourself? What if a million years pass? I am quite confident that in a million years, you will have less in common with your clone than you currently do with your own children (assuming you have children).

So no, it's not a strawman. It's a direct conclusion from where your reasoning leads. And when a line of reasoning leads to absurd outcomes, it's often time to revisit the underlying assumptions.