Politicians are some of the foremost users of logical fallacies. Political debates are created based off these logical fallacies. This is especially prevalent in gun debates.
Those that want stricter gun control laws often use the argument that if we don't ban guns then more children will be horrifically murdered. This is a perfect example of a slippery slope. There is no direct correlation between gun laws and children's deaths, yet a politician would use this fallacy to makes their audience believe that if this law is not enforced then there will be extremely negative consequences.
This can also be considered an either/or logical fallacy. It makes people believe that they either can ban guns and in essence, save the children, or allow people to own guns and are giving them the means to kill their children.
Another politician might argue by appealing to tradition. Since their father was allowed to carry a gun, and their grandfather before that, then shouldn't they be allowed to carry guns? If this was the case then any new laws would never apply. Just because your great great grandfather owned slaves doesn't mean you should. Yet this appeal to tradition proves very powerful for many people because it creates a self-righteous patriotic attitude in those that believe in it.