Where do you fit in? Objectivist or constructivist. Fancy terms for teacher-centered versus student-centered.
I like to see myself as a constructivist. I think that it is all right for a teacher to tell students they don't know an answer to a question. I think it is good for students to question. A mutually respectful dialogue is good for everyone. Students learn how to present ideas, persuade others to their viewpoint, and that people can disagree and still be friends. This furthers the idea of civil discourse and demonstrates that some of the polarizing ideas with the U.S. are not essential to our society.
Of course this could be perceived as placing the teacher in a vulnerable position. So many people have the expectation of the "sage on the stage" for teachers. How would you feel about your child having a teacher that doesn't have all of the answers? I'm perfectly fine with this idea, but some people are not. Not knowing can be viewed as a weakness. I see the ability to admit that you don't know something to your students as a strength. A teacher can easily open a discussion and let students discern the answer or look up the answer together.