You're nicely illustrating the issue with AI reasoning. Humans "reason" mostly by deciding what they believe then coming up with truthy stories to support that belief. When confronted with actual conflicting evidence or proper reasoning to the contrary, they make up more stories to "rationalize" it, or, that failing, make excuses.
The reasoning systems are generally made up of an LLM, a bunch of more general purpose neural network layers, and some conventional logic systems. The neural network part comes up with what it thinks is true based on its training, tries to get its logic systems to support it, and, as we've seen, often ignores the result when it doesn't like it.
The problem with AI "reasoning" is that it's a pretty good copy of human "reasoning."