1. Introspection is difficult.
2. Your first quote is from an advertisement from an AI company about what their AI does. It is not clear at all that it actually provides information about how it reasoned; rather, just like humans, it gives a post hoc explanation that might or might not correspond to the actual process. Get started for example here: https://www.quantamagazine.org/is-ai-reasoning-right-for-the-wrong-reasons-20260731/
3. Expert blindness makes it really difficult to explain intricate reasoning patterns to others without your expertise so that they understand. There is an entire occupation for this: mathematics teachers. Many university lecturers do not have the education for this. Some do, some pick the skill up by themselves, some do not.
4. Some mathematicians do make an effort at this.
5. You are free to get educated as a mathematician and do a better job at this than the current ones do. We are always happy when someone does good work.