Fair, you are absolutely correct. Science is in building models about how nature works. Mathematics is in the business of proving, I guess. I think we are engaging in unproductive pedantry while going away from my original point.

I want to emphasize my point again - we have 2 arguments. Argument A and argument B. A is presenting scientific evidence, in your corrected terms - presenting a model of climate change. Argument B is anecdotal evidence. The fact that they are both argued on the same stage gives the audience (who may not know anything about A or B) a false assurance that both A and B are arguable and therefore, they are on the stage. It is fine for casual conversations, I am speaking about large debates that we still fucking have about whether Earth is flat. It is equivalent of "Trolling" and should not be entertained.