Other forms: logomachies
A fight about words is called logomachy. You don't have to be an etymologist to find yourself caught up in logomachy, but you have to care about words and their meanings.
You and your word-loving friends might engage in logomachy, if you argue about the Latin and Sanskrit roots of your favorite words. There's not much to disagree on when it comes to the rare word logomachy itself, though — in Greek, logos means "word," and the suffix -machy always means "battle" or "contest," from the Greek makhe, or "fight."