Do you come back when someone rejected you?

I was dating a guy for 3 months. We were having arguments here and there. He’d always say stuff like “maybe I’ll leave you alone” or “I’ll start going to a different gym” or “I’ll cherish all the memories” like idk why he made it sound so dismissive.

Last Friday we had an argument and I said “maybe we should be friends” I said that because it seemed like everything I did was not enough for him. Like if I didn’t pick up a call ( I have only declined 1 call) or send him morning texts he would say that I don’t really reciprocate. But I was always there for him. If he wanted to see me I would go or we would meet up.

He didn’t give me a response other than he was hurt and he cared for me. He asked to hug me that same day and we lost contact forever

I took him a birthday present on Saturday and he thanked me but doesn’t talk to me anymore.

I feel so much guilt for saying that. It was just my first thing to say because I wanted to know why he ignored me one whole day over an argument so smallZ