Even if copied in the exact state, its still a copy. If this could be done without destroying the original, the concept would be more clear. What materializes 'over there' is a copy of you. I might shake his hand but wouldn't volunteer to be killed knowing that my copy will live on.
Okay ... how about this: Your little boy or girl are trapped in a high-rise apartment building that is on fire and about to collapse. There is no way to rescue them.
But there is a duplicating transporter available. It kills the subject relatively painlessly, but creates an exact copy that will remember everything you've taught her and she'll even call you "daddy".
Do you beam her up and "rescue" her?
Yes, I would make a copy of my kids if they were about to die and the technology existed.
Anyway, why does destroying the original make this concept difficult for some? If you did it without destroying the original, then you could have a conversation with your copy and know that if you died at that very moment you would no longer be conscious even though your copy is standing right next to you.