I think I might just remove the exhaust and have him fabricate the pieces for me to put on the car myself.

You know me, I am just a troublemaker. Heaven forbid people use critical thinking skills to solve problems.

I second Dan's recommendation to not do the work yourself without the right tools. I would just find a different shop. It sounds like the shop you are dealing with just doesn't want to do the job. If you have access to a welder, I recommend cutting the miniox out and either (a) replacing it with straight pipe or (b) hollowing the converter out and reinstalling it.

I'm confused now.

But that comment doesn't explain why a 2.25" pipe makes any sense considering the outlet is seemingly 2". You only get as much flow as your smallest pipe, yes?

how does someone work for so long doing exhaust and not understand this concept

I just get tired of contacting people to do a job the way I want it only to invariably be told that what I want makes no sense. It's not just this job but so many others. Why can't people just do the job you want to pay them for without trying to make you feel like you're a dumba$$?

The world is full of ignorance and incompetence. There is no knowledge test required before you can hang out a shingle selling exhaust work. Even those mechanics whose field of speciality does have some kind of a (usually voluntary) knowledge test, such as the ASE test series, often have less-than-zero understanding of some aspects of what they're working on. They profess what they think they understand of what they think they see. Often they manage to fix problems despite not really understanding what they're looking at or doing. Often…but not always.
That's a pet peeve of mine. It's one thing if you were asking for something dangerous (to the mechanic, to you, or to others) or something illegal, but the illegality of removing a catalytic converter isn't what your guy is objecting to. Nor does he appear to be taking the legitimate position that he doesn't want his name associated with work done to a sloppy or improper specification from an insistent customer. He's arguing a principle of gas flow that he thinks he understands, but doesn't. In other words, he won't do the work the way you want it done because he thinks he's right and you're wrong and/or because it's more difficult to work with 2¼"ø pipe than to work with 2" pipe.