I've thought about this a fair bit, as the idea that the clone is me never sat right with me. It always intuitively seemed it wasn't me and was instead a copy of me, that they were somehow distinct. Going off that initial gut feeling I tried to figure out why it was that I felt that way and arrived at what I think is reason for it.

I am NOT SaukPuhpet and neither is the clone. SaukPuhpet is information. SaukPuhpet isn't a physical thing, but more a collection of memories and genetics and other traits that describe a human being, but not the human being itself.

I am an Instance of the entity class of SaukPuhpet, as is the identical clone. It is not the concept of SaukPuhpet that I am attached to, but rather the specific instance of that concept, call it SaukPuhpet Alpha. In that sense the clone is not me, because I am SaukPuhpet Alpha and it is SaukPuhpet Beta. Even if Identical, we are both discrete instances of the SaukPuhpet entity class and therefore distinct.

I don't care if SaukPuhpet Beta, Gamma, Delta, and so on get to keep the greater concept of SaukPuhpet alive indefinitely, as I am entirely unattached to them. It is SaukPuhpet Alpha that I want to exist forever. SaukPuhpet Alpha is what I identify as being myself, greater concept be damned.