I was trying to explain something to my boyfriend and he said something hurtful I got upset and said something that he apparently made a big deal out of I didn't insult him though but then apologised immediately when he replied which was the next day he said something really hurtful and disrespectful I didn't reply and haven't said anything to him in days and he hasn't said anything either. Someone say something about this please

How old are you both and how long have you been together? How often have this disagreements over whatever been going on? How were they resolved in the past?

Giving someone time and space to cool off isn't a bad thing, and that's what I would suggestion without more info, or a few answers to my questions.

You sound like a very young couple, I'm guessing young teens (13-15). Adults know how to communicate with each other, even if there is a disagreement. It sounds like he said something hurtful, you said something hurtful in reply,then again, and now neither one of you wants to be the one to apologize. If that's the case, maybe you're both too young to be in a relationship at this time.

It isn't difficult for any such situation - ask him if you can go sit somewhere and talk. Working out problems isn't something you do as soon as you see each other. You plan for it. Love is not easy. And it takes real, heartfelt, thoughtful understanding, apologies, negotiations and compromises.
You could start with 'I think we both said some hurtful things, but mine was first. I'm truly sorry. Maybe we can set aside 10 minutes every night to each say what might be on our mind.'
Sound too boring and corny? Boring and corny are good.