It kills "you". Not the objective "you" of course, that lives on in the copy. It kills the subjective "you".
By terminating the stream of consciousness, the person going into the matter teleporter dies. There's no way for the stream of consciousness to continue after that point.
It's not ---------------X------------------
It's
-------------------XXXXXXXXXXXXXXXXXXXXXXXXXXX
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If you're comfortable dying so that a copy of you can live the rest of your life, that's your business. But most people don't have that sort of objectivity.