If you asked me what physical result would be naturally referred to as "the no-deleting theorem", then I would probably guess something like this:
Given a designated "blank" state $|0\rangle$ in a system's Hilbert space and two fixed states $|a\rangle$ and $|a'\rangle$ in an ancilla Hilbert space, there is no single linear map that takes $|\psi\rangle|a\rangle$ to $|0\rangle |a'\rangle$ for all system states $|\psi\rangle$.
But that's not what the actual result known as the "no-deleting theorem" says. Instead, it talks about deleting only one of two identical qubits: it says that there's no single linear map that takes $|\psi\rangle |\psi\rangle|a\rangle$ to $|\psi\rangle|0\rangle|a'\rangle$ for all $|\psi\rangle$.
This seems to me like a really weird and artificial way to formalize the concept of "deleting". Why consider only deleting one of two copies of the state? Why not one of three, or two of five, (most naturally, in my mind) one of one? Is deleting possible if you start with more than two copies of the state?