There are both constructive and unproductive ways to argue. One classic unproductive style is what Philippa Perry, in The Book You Wish Your Parents Had Read, calls fact tennis. With fact tennis, the goal can seem more like scoring points over your opponent rather than actually finding a workable solution — facts are hit back and forth until one person wins when the other has no more reasons left to counter with. But of course the argument isn't resolved and the result is a hollow victory and a still frustrated loser.
For a more productive argument we can reframe from winning to understanding — we can seek to share how we feel about it, and to understand how the other person feels about the conflict and their point of view, and take that into consideration. When we have a greater understanding we can move forward together to find a workable solution. As Philippa explains "Finding out about differences and working through them is about understanding and compromise, not about winning."