If you are having a debate with someone, that’s because you have two different arguments. Arguments are conclusion that you made based on compilation of different thoughts. These thoughts are basically variables, and conclusions are made based on combination of these variables.

Let’s say your argument is 9xy and the other part’s argument is 4xy. Not equal, hence the debate. If you go one step further, you’ll realize the variables that you are considered are 3x * 3y while the other party is 2x * 2y. They are missing some variables / thoughts that will lead them to the conclusion. Thus, one way to make the other party to have the same conclusion with you (9xy) is to fill in the missing variable; figure out to make the other party consider what you are currently considering: 3x * 3y instead of 2x * 2y. That way, If you and the other party are using the same way of processing all this variables, the other party will come into the same conclusion of 9xy on its own.

That being said if the other party use different way of forming conclusion, say + instead of * operator, 3x + 3y won’t be 9xy.

So in some sense: disagreement is basically having different variables (arguments) and/or different operator (a way to process all available arguments).