If you look around you will surely find someone making a really bad argument. There are industries that stand as little more than a totem to fallacious reasoning, there are politicians who will insist that they are right and drag their followers along in the face of evidence, there are intellectual bullies that will throw their weight around in favor of a bad proposition. Logic is the best kind of self defense against that sort of thing. Being able to craft an internally consistent argument and compel others to follow along with out resorting to trickery is properly part of engaging in a productive debate. If we are going to live together in a society we have to be able to rely on each other to go for what is properly the best idea rather than simply listening to the loudest voice.
Our country was founded on logic and reason, the founding fathers sat down and discussed the different ways to build a country, to build an empire, they didn’t just listen to the loudest men in the group.
The reason we have public schools is a three fold one. In order of importance: First, they act as a daycare program for working parents, instead of every parent having to pay to have their child looked after or having to take them along to work and suffer a loss of productivity a teacher wrangles them for several hours most days. Second, a more educated populace is more productive, by sending kids to school we increase the percentage who receive education (while possibly reducing the number who get very good education) and that increases literacy and numeracy and that increases productivity; by increasing productivity we help the economy. Thirdly, we help ourselves toward a more informed electorate. This is why we have history and government and civics classes in schools, to help people avoid some of the political pulls that await them (after all, what better argument against communism is there outside of the history of communism?) in the real world.
This last one was the argument used by Thomas Jefferson, and it would be first on the list if it worked a little better. Most of the problems of our society can be made better with better government, and government can be made better with better voting and better citizen involvement.
Logic classes in school are a means towards that end. If we all thought critically, and strove to avoid using bad arguments, we would be less likely to make mistakes, less likely to support the corrupt, and less likely to divide ourselves so violently on many issues. In short a little logic could make us a more harmonious society, and teaching it in school like long division could make it a tool that every student gets to carry around with them to succeed.