My best friend (24M) and I (23F) had a huge fight and he doesn’t want to be friends anymore?

Anonymous
My best friend and I had a huge fight a little more than a month ago and he said he needed time to process things. However, I gnatted a lot and 2 weeks ago he said he got really mad with me, saying he has felt tortured and can’t stand it anymore, he said he doesn’t know how to make himself care about me again and see me as a friend. I stopped texting him and decided to go into NC for some time, but we saw each other a couple of times at the gym and he greets me every time he sees me. He also wears a bracelet I gave him after the fight (I had purchased it before the fight but received it after we stopped talking). I’ve apologised many times but I feel like he will never forgive me (I made a lot of mistakes and I deeply regret them). I told him I’m gonna change and eliminate my negative traits but he doesn’t seem to believe. I’ve decided to send him a letter maybe a month after the “break up”, saying how much I love him, how much I’m sorry, etc, etc (I’ve already written it and I think it’s very emotional and poetic and it will make him feel something) but I’m scared of what will happen. Do you guys think sending a letter is appropriate in my situation?
My best friend (24M) and I (23F) had a huge fight and he doesn’t want to be friends anymore?
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