When someone replies to a statement you made by calling you names, they're implicitly saying that's it's true. Otherwise they could have shown why you were wrong.
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Ad hominem means when you attack an argument based on the qualities of the person making it (e.g. "Of course a Catholic would say that."). Dismissing a class of statements could be mistaken, but it is not an argument ad hominem. https://en.wikipedia.org/wiki/Ad_hominem
Clearly it's not ipso facto wrong to dismiss classes of statements. Anyone who describes a logical fallacy implicitly does this.
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If someone calls you a name, that's an ad hominem. It really has nothing to do with the truth of their argument. You dismissing such arguments on account of the impoliteness of the other person is an ad hominem rebuttal.
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It would be one thing if you only said you don't like arguing with people who insult you. But your original statement even goes as far as to reject the person's argument, whatever it might be.
End of conversation
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