Imagine you are destroyed in your sleep by aliens and replaced by an atomically identical duplicate. Would you call this "you"?
If not, what if the aliens recycled the atoms from your original body to make the new body, putting each original atom into the same original spot with the same position and momentum (ignoring quantum and uncertainty principle).
What if they recycled 99% of the atoms from your original body, but swapped 1% of them for different atoms?
What if they only destroyed 5% of your brain and reassembled that destroyed portion, leaving the rest of you untouched? What about 50%?
What if they waited 1 planck moment before reassembling you versus 5 seconds?
Where is your dividing line in this scenario space between "that's really me" versus "that's just a copy and is not really me" ?
The functionalist answer, as I understand it, is fungibility across time and copies when arriving at definitions of words like "you".
The functionalist answer is not that > 1 copy can communicate telepathically or supernaturally share experiences is a dualist sense. They are still causally independent physical entities.
None of these scenarios would result in "me" from a monist perspective. The destruction is a discontinuity point, I died there and then, and then the next planck moment a new being was created with all my memories. But "I" died.
The functionalist answer, as you understand it, is dualist. It says "something" survived the utter complete destruction of the physical body and was "put back in it" once it was reassembled. If "it" survived the complete physical destruction of the body, it must be somewhere else, detached from the body.
And, you know, there's really nothing wrong being dualist. I do not mean to denigrate that specific worldview. What is problematic is claiming to be a staunch monist while holding dualist positions.