"... I hope that was a joke. What do you propose ..."
I would propose, 'ill-logical'. Using foreign phrases in English where a simpler one suffices, makes for harder reading. It is often used by writers to impress, or prop-up arguments. There are quite a few readers who are reading English as a second or third language. Let the ideas come forward instead of the language.
"Illogical" is vague enough to be useless, and is rarely used in conversation except by Mr Spock. "Non-sequitur" is a very specific form of illogic, appropriate in this case.
I'm sorry if there's anyone out there who doesn't understand "non-sequitur" -- admittedly a Latin phrase but one that's fairly well incorporated into the English language. But I really don't think it's obscure, especially by the standards of the kinds of obscure conversations which this site is filled with.
For what it's worth, I actually remember where I first learned the term "non-sequitur". It was in Mad Magazine when I was probably eight years old, and I was reading an article about (I think) "Parental Non-Sequiturs". If it's good enough for Mad Magazine, it's good enough for me.
I would propose, 'ill-logical'. Using foreign phrases in English where a simpler one suffices, makes for harder reading. It is often used by writers to impress, or prop-up arguments. There are quite a few readers who are reading English as a second or third language. Let the ideas come forward instead of the language.