In my experience, beginning math students simply expect their nice-sounding procedures to work. For example, they expect to be able to add fractions straight across. When you tell them they can’t, they demand to know why they can’t, as though most nice-sounding theorems are true, and if you want to claim that one isn’t, the burden of proof is on you.

I've noticed that, on the few occasions I've taught genuine beginning-beginners. Never thought of it in that many words, but yeah. And the analogy to beginning rationality students, including 50-year-old scientists making up their own religions, is obvious and important. People starting out in math are operating in "sounds nice" mode, symbols with no consequences but their poetic resonance; and if you challenge their poetry they act all indignant, "Why's yours better than mine?" 50-year-old religious scientists never leave that mode.