Now that you've reflected a bit about this, I'll get to the part about why this matters in our relationship. Conflict or arguments are an unending part of a relationship or marriage. Yes, it's an ugly reality. So it's unrealistic that we can prevent or escape conflict. Conflict in itself is not bad for a relationship since it can help the relationship grow and strengthen bonds. However, if conflict escalates beyond our control and repair attempts don't work, then we're left feeling unhappy in the relationship. And each time a conflict escalates without repair, this unhappiness builds up. So the repair attempt is key in stomping out unhappiness and helping move towards more positive feelings.
The great thing is that repair attempts can be as creative as you are and personal to your relationship. There is no "one size fits all" approach here or even a "what works best" approach. Since each relationship is different and everyone responds differently, the repair attempt you use with your partner is going to be unique to you. For example, I worked with a couple in which the husband would use humor and say "you can hit me here if it makes you feel better" and point to a part of his body. This would quickly de-escalate his wife's anger to laughter. Did he risk getting hit pretty bad? Yep he did, but most times it humored his wife and took the focus away from the anger/tension that was building.
Relationships with conflict are not doomed and are often not broken. But they do need help getting back on the right track and repair attempts are the way to get things back on track.