Scientists use advanced mathematics, while ordinary people use simple math. Without knowing it, you use simple logic throughout the day. No, that is psychology the study of the way humans think and feel. The science of logic has more to do with arguments themselves. Logic is the science of correct reasoning.
Logic teaches standards for how to discern good reasoning from bad reasoning.
This is not a problem with logic. This is a problem with the way people argue. There is no reason to be afraid of logic. There are times I have pointed at my mother and criticized her for how illogical she was. Instead, I should have been looking back at myself and criticizing my lack of concern for her feelings.