Logic is important because it allows people to enhance the quality of the arguments they make and evaluate arguments constructed by others. It is also an essential skill in academic disciplines, such as computer science and mathematics.
When a person argues logically, he's more likely to convince people of the validity of his claims or get them to agree with him. Even if people are unable to pinpoint a fallacy involved in an argument, they can detect the argument's invalidity if it’s constructed illogically. Familiarity with logic means that one knows how an argument should be constructed and also what constitutes a bad construction. Thus, logic protects people from being swayed by bad argument.
Students pursuing computer science or mathematics apply logical reasoning to arrive at inferences. In inferring, one justifies a claim based on a collection of statements called the premises. With deductive inferences, the conclusion must be true if the premises are. For instance, the Pythagorean Theorem is proven true after treating the postulates as true in elementary geometry.
In society, one has to use logic or evaluate an argument when she's being persuaded to buy one type of car and not the other, vote for politician A rather than B or adopt a given social policy.