Ironically, it has to do with what I've been mentioning from the start - paradigm shifting and see truths (plural) rather than truth (singular). Or put another way, choosing and shift what one believes at will. A reason I have a problem with your use of extreme examples is that it deliberately polarizes the conversation. That is not the angle I am taking on this. As has been said before, the relative ease in which one can paradigm shift depends on how attached someone is to a particular idea, or how fixed and entrenched one's thinking is about something. On the whole, I'm not the sort of person who is attached to sets of ideas; on top of that, my ontological philosophy is such to support ease of paradigm shifting. I've got my default maps of the territory like everybody else does, but I like giving other maps 'screen time' so to speak. I find exploring other ways of seeing fun and interesting. Hence, I can sit here, find your points reasonable (with respect to your map of the territory - the set of things you choose to believe), then still look at other maps and go "well this map says this, and I choose to believe this most of the time."
Ah, here's one of the rubs, I think. What is reality? Do you believe you're holding the territory, or are you grasping a map?
Wow! That's how you approached this? No wonder you've taken to examples that are ridiculous and extreme to me! You presumed that this paradigm shift requires altering one's entire understanding of math, or one's "grasp" on "reality" (whatever that is)? Really? Wow. That is not how I read it at all.
Brings up an important point: the difficulty in paradigm shifting is very much dependent on the assumptions one brings to the table or how one approaches the map of the territory. Also depends on things mentioned earlier, and some things not mentioned yet (probably).