A critical thinker is someone who is in the habit of challenging statements. To challenge a statement is to look for a reason to believe it. Challenging a statement is not the same thing as disagreeing with the statement. Indeed, critical thinkers are in the habit of challenging their own beliefs, not just the statements of other people.
When two people disagree about a statement, one asserts that it is true while the other asserts that it is false. People disagree with each other all the time without doing any critical thinking. You might say "The Pirates are going to win the conference this year." I might reply "No, they're not." Neither of us is acting like a critical thinker because neither of us has looked at any reasons that might support either statement. We are just stating our opinions. We are not backing them up.