I'm a busy man, so this will be a short one. Comment if you require elaboration.
An argumentum ad hominem, to borrow from wikipedia, "is an attempt to negate the truth of a claim by pointing out a negative characteristic or belief of the person supporting it."
The specific data point people need to take from this is that an insult is not by default an ad hominem.
Also something I want to try to mention every time I bring up fallacies: if an argument contains a fallacy, it is not by default wrong.