Critical Thinking does not mean arguing, or tossing quotes or statistics back and forth. It means being willing to listen to and understand the issues, opinions, interpretations of the facts and issues. It may require reading entire books, seeking out original writings and recordings that go beyond soundbites and quotes, talking to people on both sides and working toward compromise, or at least solutions that can work for both sides.
Being willing to listen, to understand and to see the value of the other side of the equation has long been a vital part of decision making, of reasoned discourse and of needed compromise for society to function and individuals to understand each other and other cultures or ideals.
Critical thinking refers to higher order thinking that questions assumptions, your own first and foremost, and those of opposing views or of generally accepted realities.
By questioning your own assumptions and beliefs, you open yourself to discovery of not just information or perceived "facts" that may contradict your beliefs, but also information that supports what you already believe. You will be less reliant on what you are told from above, or hear on the news, or hear from friends who often repeat things in different ways (think of the old game telegraph). You become a part of the solution and not the problem.
Critical thinking is not about fighting, shouting heads, or openly confronting others. It is about challenging others, teaching and being open to learn in your own right.