"I'm finding it hard to meet his logic with further logic."
You're not going to be able to, OP, because this whole situation is not about logic. If it was, many more of us would be choosing not to have children at all. I am actively jealous of couples who are certain that they don't want children. What a boon! All that money and freedom, with no lingering sadness at not having kids.
But that isn't your situation.
But to edge into logic territory a little: your DH needs to play the long game. Another thing people don't like talking about: people get old. And while we can't expect our children to help us more and more as our years increase, wouldn't it be nice?
Tell your husband to take a look at your child: the little kid who has just started school. That person will, in all likelihood, be bearing the load of your old-age care in decades to come. Easier alone, or with a sibling? What does your husband think? Because that is a reality that many people are living. My DH is one of them. When his remaining parent passes away, he will be organising their funeral, sorting their property, the sole guardian of all those memories.
I realise I sound maudlin but that is the reality. Does your husband realise that he is being fairly selfish?