What should discourse have that it often lacks? Logic is not “what seems reasonable” or “what feels right.” Like chess or mathematics, it has a strict set of formal rules. We use logic to show the connection or lack of connection between concepts. It is machinery into which we put our perceptions and values. Used correctly, it has an important role in quality discourse, but it is not the totality of discourse. Logic bears on how we express ideas, but it does not determine the ideas we express. When we make meaningful arguments, there must be proper and improper ways to interpret and understand what we say. If we do not make the boundaries of our statements clear, they may be interpreted liberally. The more possible interpretations a thing has, the weaker its effective force as an argument. (Note that excellent fictional prose or poetry often lauds multiple interpretations. Also note that arguments of formal logic are a very different sort of poetry.)
This touches on the greater abuses of statistics and imagery in everyday arguing: statements that sound large but are undefined and unbounded. You may tell me a tremendous-sounding statistic, but without context. You may show me a striking photograph, but without significance. All too often, we are given a sound bite or image and expected to “see” some inherent rightness or wrongness. Good arguments are more than only conclusions; they explain what is being asserted and upon what grounds such an assertion could or should be believed. (Some may cringe at my glossing over the “belief is not closed under implication” issue. I sympathize, but just go with the shorthand.)
Perhaps the greatest threat to good discourse is assuming the speaker advocates the opposite of what he argues against. (e.g., when I criticize the way “privilege” is used in debates about race or gender theory is bad, people assume that I favor oppression of others or fail to see it.) This makes it hard to have clear and careful discussion about sensitive (emotionally charged) topics. By making assumptions about the position of the speaker, we forbid constructive criticism- and therefore the growth- of progress on important issues. Avoiding logical fallacies is not a neat academic trick without relevance to daily conversation. Just as the rules of mathematics or science or language can help us in real ways, logic can help us better understand ourselves and each other, and make progress in debates and discussions, and avoid misunderstandings and unintended offense.