Thinking critically does not mean trying to find weak points in a concept or idea. Your goal is not to make others understand they are wrong but to learn how to be objective and ask the right questions. Having this skill is highly significant in the modern society. Due to the abundance of information you get every day, it is difficult to check if the facts you learn about are actually valid. People can wangle statistics and manipulate. They can make others believe something is true when it's not. Critical thinking helps you assess the validity and meaning of the information. You will be able to evaluate the arguments of others and decide if they are enough to convince you.
Unfortunately, it is impossible to gain the universal knowledge of thinking critically. Every one of us will still rely on personal experience and have some blind spots in reasoning. The process of validation depends on the level of our domain expertise in a particular subject area or class of questions. The presence of self-delusion is inevitable. It is often that our brain makes us believe in something that never happened. Like, for example, it is in the case of witnessing a car accident.
Every witness will have different memories of it. Some will say that it was a man driving a red car, others will be certain it was a woman. As to the critical thinking, it is always our past experience we rely upon when making judgments. If you learn how to make a few steps back and look at a situation from another perspective, you might see many new pieces of a puzzle that complete the whole picture.