Boyfriend won’t hold my hand in public

I have a pretty serious relationship with my boyfriend, but every public place we go to , mall, store, even to like a restaurant he won’t hold my hand, if I’m on the left side of him he puts that hand in his pocket, or holds things like kinda avoiding holding my hand. Now I’ve talked to him before about this and that was three weeks ago, he said he would and didn’t know it made me upset. Well nothing changed. He said we aren’t in a 13 year old relationship and we aren’t 5. He says people will think if I’m standing beside him were together and we don’t need to hold hands. We are 18. It really hurts and I hate going out to public with him because I follow him around like a little puppy. It genuinely makes me upset. probably me being childish but every boyfriend I’ve had holds my god damn hand everywhere. And I would honestly dump him over this.