My understanding of what makes these types of counterargument persuasive is a belief system that goes roughly like this:

I comprise a set of attributes. For convenience, I categorize those attributes into two sets, S1 and S2, such that the "teleporter" preserves S1 but destroys S2. What comes out of the "teleporter," S1, is similar to me but not identical; the difference is S2. S2 is so valuable that even an X% chance of preserving (S1 + S2) for some very low X is more valuable than a 100% chance of preserving S1.

My own response to this is that I see no reason to value S2 at all.

But I accept that other people do.