Most Helpful Guy
If you're both cheating on each other (at age 13?) then you don't really need to be worrying about who has the better position to argue from about breaking up. You just shouldn't be together to begin with. If you're both cheating on each other, the relationship has failed and you both need to step away from it and do some self reflection before moving on.
Also cheating isn't like a drug you can be "clean" from. It's an indelible marring of the trust you form in a relationship. If they supposedly forgive you and then cheat on you instead, they haven't done much forgiving, and there isn't much trust there to begin with between either party.
Most Helpful Girl
You have the right to get mad, but if you keep cheating on eachother it's probably a sign you are not right for eachother.