Logical thinking is a method of rational reasoning used to eliminate subjective influences. Decisions can often be altered because of emotional or cultural biases, and logic is used to move closer to a truly objective reasoning process.
For example, the current political climate in the United States is largely driven by emotional and cultural biases. Partisans on all sides argue from a platform blinded to reason because of group-think, the tendency to agree with peers without consideration of other facts.
By studying logic and examining the methods of pure rationality instead of personal bias, we are able to bring our reasoning process closer to a truly objective position. Logic is also extremely important in science and mathematics, where bias has no effect on reality; debate can convince people that 2+2=5, but it will never actually be true. Logical reasoning is the most important part of an honest debate system, as it avoids ad hominem attacks and other logical fallacies, which serve to divide opinion and avoid actually resolving an issue.
Regardless of personal beliefs, logic will provide the same solutions more often than not. By learning to think critically and use rational logic instead of emotion, decisions and opinions can be based in fact rather than in bias.