Why does it matter if he has a child? Because it makes a purely emotional argument less effective on him?

Talking as someone with 5 siblings (4 brothers, 1 sister), I find that one brother is generally as good as another whereas my sister is unique.

Based on this, your question of "Are you an only child?" seems only to be helpful to your argument when used against people with a relatively small amount of siblings of a particular gender. This condition is, let's be honest, a relatively new development in the first world and simply doesn't generally exist in the developing world.