There are those people who argue in order to debate, inform, and seek the truth, and those are the ones you should spend time arguing with.
But there are many people who use debate not as a tool to exchange information, but to flood the world with their misinformation. They will change positions, use falacies, and speak without ettiquitte as long as someone is listening.
That person's goal is not to argue for a purpose, their purpose is to have an arguement. It does not matter if they win or lose, they just want to have muddied the waters and leave spectators remembering that "there is legitimacy in arguing over this topic". (See flat earthers, neo-nazis, ancient aliens, etc).
In short, arguing with them only benefits them and harms you and any spectators. Dismiss them for the jerks they are and focus your efforts on those who are genuine in their approach.