How to get her back?

Hey guys,

To start things off, we’re both 23 and have been dating for almost 2 years. We had made plans to get married, to move away together, and be together forever. As with many relationships, when times were good, things went exceptionally well. However, when there were arguments which are inevitable in every relationship, things can go south very quickly. I’m not going to slight my ex-girlfriend, but it’s probably attributed to the fact that we’re both proud and stubborn. The pattern for us occurs almost on a monthly basis, as follows:

1) There would be an argument about something minor, maybe toothpaste or groceries
2) She would demand her way to be kept, and that things should be done her way. She would sometimes get agitated and swear at the overall situation
3) Although I would try to comfort her and resolve the situation as (2) is happening, I eventually get upset myself and lash back at her
4) If this happens in real life, I walk away from her. If this happens on text or phone, we both stop texting each other for about 2 days
5) After 2 days, I miss her a lot and either one of us reaches out to the other, and I spend about a week begging for forgiveness, which she has given to me until this time

So the issue here is that she thinks I should always be the one to reach out to her after a fight, regardless of who is at fault. I know that everything is subjective and can be perceived differently, but what do you guys think? Normally the issues start at 50/50 fault and does not even matter much in the whole scheme of things, but by the time I try to save the relationship and reach out to her, it seems like it’s 0/100 stacked against me. Is it a standard in most relationships that the male reach out regardless of who’s at fault, and to swallow the pride and try to reconcile it?

If so, do you guys have any tips as to how to do it on a consistent basis? I have succeeded, and I have failed, but unfortunately the failures are much more memorable for her than what I succeeded.

Appreciate you guys reading this, thanks.