Not sure if you were trying to be snarky with the lmgtfy but that didn't actually bring anything up.

Look at this: http://en.wikipedia.org/wiki/List_of_fallacies

I quickly looked through them and didn't find anything directly relating to symbolic logic. Most of symbolic logic was trying to understand what was at first pretty confusing notation and then trying to figure out how to represent things like sets without using Venn Diagrams.

At the end of the day I don't think you start to understand any larger truths about logic. Knowing how to write out De Morgan's law with symbols is frankly kinda useless.

Maybe it helps with mathematical thinking, but that's not relevant to most people.