An explanation, then a couple thoughts:
We find it justified to take children away from parents who we consider "guilty" - adults who can take on such a serious duty, but who then make decisions which fail to fulfill that duty. Neglect and abuse are considered to be the result of such decisions, while poverty is considered to be (often? always?) the result of bad luck. Teen parents aren't considered candidates for this level of guilt for the same reason that their partners might be considered candidates for statutory rape charges - it's presumed that teens are too young to be making mature decisions about sex.
If you really want to step into all your opponents' shoes, you need to consider that some of their models of the world aren't just "zero meritocracy", they're "moral anti-meritocracy", i.e. "rich people got that way by being more willing to step on poor people".
Specific policy implementation details might be seen as less offensive than the policy they're intended to promote. E.g. a progressive who currently considers you a eugenicist monster might nevertheless already be your ally for a few practical purposes, like subsidized access to birth control, and you might be able to talk them into others, like switching the estate tax exemption level from a per-estate to a per-inheritor amount.
Neglect and abuse are considered to be the result of such decisions, while poverty is considered to be (often? always?) the result of bad luck.
The bigger difference is that neglect and abuse are carried out after children are born, while poverty is usually there before they are born. Prospecitve parents are much likelier to correctly predict they'll be bringing up poor children, than that they'll be bringing up neglected or abused children. And for the same reason, it's much easier for society to predict who'll be a poor parent, and disincentivize them,...
I recently read an article by Steve Sailer that reminded me about something I have been puzzled by for a long time. Relevant paragraphs:
Poor people having fewer children means that the children have more resources available per capita making the children better off. Rich people having more children actually increases equality in society since it reduces the per capita resource advantage their children have. Rich people giving to their children is also one of the few cases where the redistribution of wealth doesn't reduce incentives for wealth creation. Rich people care about their children too.
Since programs aimed at reducing teen pregnancy rates do seem to have had some effect, we known something like this is possible without being horrible to the potential parents it targets.
Yet a policy of "poor people should have fewer children, rich people more" sounds heartless despite increasing general welfare both by making poor children better off and by reducing the privilege of rich children thus increasing equality which we seem to think is ceteris paribus a good thing.
Why is that?
Edit: To test the source of the reader's intuiton (assuming he shares it with me), I encourage the consideration of two interesting scenarios that may depart from reality.