The apparent concern that these comments show for the well being of children is misdirection and rationalization, hiding the true intent behind anti-natalist perspectives, which are fundamentally eugenic in nature.
At their foundation, these comments presume that there are people who deserve to have children, and that there are people that do not—in other words, that there are children that deserve to be born, and that there are children that do not deserve to be born.
Poverty is just a proxy for other qualities that would be much too controversial to articulate explicitly.
And I think you misrepresent the potential harm. Anti-natalists don't just want to forgo having children. Many anti-natalists also want to discourage or prevent other people from having children. In fact, I'm sure many people making anti-natalist comments here do intend to have children themselves—they just want to discourage or prevent other people they find undesirable from having kids.