In conflict, it is important to address the arguments, not insult the individual. If your goal is to merely discredit an individual and not resolve the conflict, then what are you doing to help a situation? It is impossible to agree on everything with another, just as it is impossible to disagree on everything. In an argument it is imperative to stick to the issue at hand and not go outside that boundary.
Am I perfect at this? No. In the heat of the moment it is easy, and ill-advised, to attack the individual (i.e., ad hominem). But it does not solve anything. Though honest conflict is superior to faux peace, it is disingenuous to enjoy conflict. The best mediator is one who can remain objective, admit fallibility, and honestly want to resolve a problem. As human beings we are equal no matter the differences.