Hello Joseph,
He never said that. It’s a subtle difference, but the actual words in the sutta you quoted are “No self exists for me”, or, as I like to translate it, “I have no self”.
The problem with this reflection is not the “no self” part: it is the “for me” or “I have” part. Having the idea “I no self” still involves a sense of self in the “I”, so it’s still wrong. Notice, though, that the idea “there is no self” is NOT mentioned to be wrong. In fact, there are various suttas that clearly indicate that this “there is no self” is exactly the right view. A clear one is MN22, which states among other things that “those who mourn the loss of the self they mistakenly thought they had, mourn the loss of something that never existed in them in the first place”, or Dhammapada 62 which says “atta (attano) na atthi”, “there is no self (for him)”.
For some connected ideas see here: Bodhi vs Ṭhānissaro debate - #89 by Sunyo