1. Good rebuttal. No, seriously, proof by dogmatic assertion is great.
Of course it causes all these things. If you're refusing to modify existing code, then you can't refactor it to handle extra cases, which is going to lead to unnecessary duplication (and probably hideous cut/paste code). It will expand the size of the codebase, because this is what happens when you add code, which will eventually cause problems on some platforms (trust me - I've been there).
2. Turn in your coding license. Now. Except for a very small subset of coders working on very specialised projects and using formal proofs of correctness, anyone who claims their code contains (or should contain) no bugs when first written is a fool, and a dangerous fool at that.
3. That may be your experience. Rolling back version control history to find out where defects were introduced can be very useful, and if the tools are good enough (which they are) it isn't exactly difficult either.
As for the idea that you can't track all dependencies from the deleted code to the whole system, if that's true to the extent that you claim then your design is screwed.