If you want it to synthesize information that is not in its training data (from a few months ago), you can ask it to research the topic. But, arguing with an LLM is like putting lipstick on a pig. Only the machine is incapable of becoming annoyed. It has infinite patience to continue being wrong forever.
Your mental model of what Claude is and does is the problem here. Short of a revolutionary breakthrough in AI techniques, the LLMs will continue to do matrix math across a huge bunch of weights that cannot change based on anything you say.