It's not exactly that, the GP isn't claiming something the parent didn't say, they're just treating the example as the whole point. They act as if attacking the example invalidates the whole argument, when the point clearly stands and it's trivial to just find a better example.
Yeah it would be nice if there were a more specific word, but I think this still qualifies as a straw-man. It misrepresents the argument as a whole by acting as if refuting the "your kid" example refutes it completely.