What the soldiers hear
What the soldiers hear
It is not an argument, it is a joke comment, it is not trying to persuade anyone of anything. It is a lighthearted joke.
Making a comment about someoneās writing style isnāt ad-hominem, also the original comment didnāt make an argument at all, it just said that your opinion is wrong, which is a joke as an opinion literally canāt be factually incorrect by definition. Here is a pretty good resource for learning about ad-hominem in practice.
That being said, you also fell into the very common fallacy fallacy.