Ad hominem is an idiom: you cannot infer the meaning of an idiom from the composition of its words. A counterargument is ad hominem if it rests on what it says

Ad hominem is an idiom: you cannot infer the meaning of an idiom from the composition of its words. A counterargument is ad hominem if it rests on what it says about the arguer, not the content of the argument. It's not always a fallacy, but it is a danger sign for bad argument.