Nature of disagreement in public debate

In my argumentative writing class, we are reading a book called "Ancient Rhetorics for Contemporary Students," by Sharon Crowley and Debra Hawhee. In my blog today, I will begin with a passage in which Sharon Crowley writes,

"Because knowledge originates with human knowers, and not from somewhere outside them, there is no absolute truth that exists separately from human knowledge. Moreover, contradictory truths will appear, since everyone's knowledge differs slightly from everyone else's, depending on one's perspective and one's language. Thus Protagoras taught that at least two opposing and contradictory logs (statements or accounts) exist in every experience. He called these oppositions dissoi logoi."

Protagoras was a Greek philosopher who believed that there is no absolute truth, but only the truth as each individual perceives it. In other words, one might say there is no right or wrong. A person's perception of the truth may be impacted by ether their individual perspective or their language as it relates to a specific topic. Perhaps a very simple example that my help illustrate this point: Let's say you want to argue the thesis (truth) that "it's good to have a dog as a pet" based on your experience with dogs. Some people may argue that your "truth" is wrong because they have different perspectives. Perhaps they've been attacked by a dog, or they're allergic to dogs. Other people may argue that your truth is wrong because of cultural language or definitional differences. In some cultures "dog" may refer to a wild vicious wolf that no one in their right mind would want to have as a pet.

Of course the statement that "absolute truth" does not exist is somewhat comical since that statement in and of itself could be considered a statement of "absolute truth," and so the circular argument continues! Because people generally believe that the purpose of debate is to convince either the opposing side or other listeners (as it is in public debate), if you accept the theories of Protagoras or Cowley, one might ask what the purpose of debate would be given that there is no absolute truth or right or wrong, and consequently, there can be no winner or loser. In very simple terms, if everyone were to agree that there is no absolute truth, then why bother debating issues?