You are thinking of a very specific scenario of debate where knowledge is merely a set of observable/observed facts and everything in the discussion is fully described, strictly bounded and available for scrutiny.
In such a "sandbox" of logical positivism, sure, one can see a debate as an unfolding of consequences from logical primitives.
That's very far from what most actual real-world debates are like. There's typically a profound lack of facts, knowledge and experience. Deciding something like "how to proceed" with a business decision involves dabbling in a lot of uncertainty, subjectivity and emotional baggage from both sides. Subjectivity is often a dirty word amongst software developers but, outside of stackoverflow.com, it's fundamental to human experience and argument.
Though, it's possible to keep arguing after by challenging the internal consistency of the other person's assumptions. You can often win arguments by demonstrating that their set of assumptions leads to a illogical and contradictory result, or you can show how their assumptions prove something that they don't agree with.