When two people are together, they choose to compromise for the differences they have between one another. Those differences often lead to arguments and disagreements, and that is completely normal. You cannot expect two people to be together, and not fight at all. However, sometimes, those fights and those arguments begin to get dragged. They should end quickly, but when they get dragged, they create a lot more problems. Here are a few ways through which you can end an argument:
Do not take things to your ego.
To end an argument, the first thing you need to do is to stop taking things to your ego. If you are going to let things go, it will not hurt your ego. You have to let some things go, because if you hold on to them for long, they will strain your relationship. If your fight was about how they left the house dirty and you brought friends over from work to that dirty house, then lecture them over it and leave it. If you keep focusing on how embarrassed it left you, you will not be able to forgive easily.