you took a quote of a snarky comment, assumed it a correct reproduction, and then suggested it's the result of imitating adults along with a (sad) state of affairs caused by adults (parents in this context), further implying that snarky comments are the general rule in the house.

now concretely: Your conclusion doesn't follow the evidence (non sequitur).

You made a generalization (inductive inference) based on a single datapoint (here's where my pointed faulty generalization or inductive fallacy are the come in) for the general problem. I suggest Popper if you want a deeper treatment of the problem of induction (The logic of scientific discovery is a good start).

Besides generalizing for free, you cooked up evidence that didn't exist - mainly that the child was imitating adults (again, non sequitur).

As a side note, I think it's in poor taste to make remarks about someone's children in what's a technical and informal context. That may have not been the intention but, it's what it looked like.