Arguments generally are two sided and a sign of maturity is that we can forgive and also accept responsibility for our part in the fight.
I think more than this though, forgiveness is absolutely essential for our own mental and emotional freedom. Carrying a grudge, resentment or anger does us more harm than it does to the one we perceived to have wronged us and it traps us in the past. Breath, move on and be free!
P.S. I think if you can forgive others first, forgiving yourself will be easier since you have done something to earn it. The price we pay for forgiving ourselves could well be accepting the flawed humanity others?
Yes, I always begin with myself. There is something with accepting your self just the way you are, flaws and all! And when I forgive and accept myself, it's easier to forgive and accept others.
Thank you for your lovely comment! @burtybasset
Welcome. Have a great day!