Is this a phase? No.
Until you get to the root of your arguments this will continue happening, it won't just go away.
You even mention here that every time you try to talk about it, you DON'T get to the bottom of it, and it keeps happening. Well, I'm going to tell you right now that these fights are going to be the demise of your relationship unless you get to the bottom of the issues.
You state that you have fights over stupid things. Why are you arguing? When you're in a relationship both people need to learn to pick and choose their battles. 95% of the time, the stuff you get annoyed over and start a fight over, is not worth the fight. Sometimes you need to bite your tongue and move on. If you guys keep dwelling over the stupid things, and fighting every day of every week, it only shows what a weak foundation you guys have.
You both need to learn how to communicate without arguing. I used to be like you, I would flip out over the stupidest sht and then wonder why my relationships never worked out. Instead of talking like a civil person I would get angry, throw fits and just be ridiculous.
I've been with my current boyfriend over two years now. We have NEVER had one fight. But I'm 27. Do you know how long it took for me to learn how to get my point across without fighting? Without arguing? Fighting does not strengthen a relationship. It weakens it until it just collapses. Believe me my boyfriend and I have been through tremendous ups and downs, but... no fighting.
Both of your stubborn personalities are not good. You both need to drop the ego's you have. Being stubborn is not attractive, and it's not a quality trait to have. Until you both realize that being stubborn isn't a GOOD thing, the sooner you guys could possibly resolve this. You both need to back up, open your ears and listen to the other person. As you probably know, if you have opinions and he has opinions, just shouting them back and forth at each other does nothing.
Perhaps you guys are just not compatible on that level. Some people despite being in love, are just not compatible in a relationship. If you just keep butting heads, that's unhealthy, and if it can't change, then you need to just end it. I think you're both highly immature and that's why you're both unable to get over yourselves to back down and just listen to each other.