My goal is to come out with a plan that works best. That almost always involves taking criticism and advice into consideration, and sometimes involves not doing things my way. Sometimes I'm even completely wrong. But sometimes I'm completely right. There's no way to know before having the "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.
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.
My aim is always to try and understand a different perspective, because this forces me to account for that in my own perspective.
My mind can be unchanged or I can 'win' the argument and still have learned something new with this approach.
Of course the above is a big if. I don't think I've ever done it. But that is my goal.
Most of the time though you are right, I want to find the truth which might or might not be what I think it is.
I have, once. Or at least I came close. The lady had two arguments: vaccines, like most medicine, make our immune system weaker; and "they" put poisonous stuff in vaccines. I pointed out that (i) vaccines aren't a crutch that may relieve or replace our immune system, but a kind of kick in the butt designed to strengthen our immune system, and (ii) that yes, they put poison in it, because that's how we can ensure our body reacts to it and prepares itself for the real thing.
That was enough to cause her to reconsider her conspiracy thinking. I think one key here was to acknowledge one of her arguments (the poison thing). I also did not discuss regular drugs, so I could focus on vaccines. I did not deny drugs makes our immune system weaker, even though I don't think they do in most cases.
Turned out listening can be a rhetoric weapon as well as a learning tool.