On the flip side, "think of the children" does not necessarily mean the argument is without merit. There are countless debates in which it is a valid point. For example, climate change is a big "think of the children" issue because the impact will be felt greater by children than by the people who are currently in power. I think some people have become too cynical and see a "think of the children" argument and reflexively take the opposite stance in order to be contrarian. It is basically the fallacy fallacy[1] that you see all over the place, especially in debates on the internet.
[1] - https://en.wikipedia.org/wiki/Argument_from_fallacy