School help

So, I just got silently disappointed today at school. In our geometry class, I was asked the question by my teacher: True or false, all chords of a circle contain exactly 2 points. So, I answered: false. My reason (I didn't point this out): Well, the center of a circle is a part of the circle, if a line intersects an existing point (the center of the circle in the current case), then it contains the point (i might be wrong), and a diameter is a chord. So, my mind told me to answer False since the diameter is a chord, and it intersects the center of a circle, thus containing it. My teacher had that scary look at me, and began to incorrectly explain to me that a chord contains two points. I am a very inconfident student, I only speak when I'm mad. She began to tell the class about people who think they're always right that was very sarcastic on my view.That moment, my teacher was clearly behaving unprofessionally. She even told me that I cannot accept what is said to be right. I was supposed to tell her that I am a person that believes logically, you can't just tell me something is right and that's it, you have to explain a reason. But then she continued and had that unwelcoming face. She clearly was influencing close-mindness to students, overprioritizing discipline. Anyways, even though I could be wrong, her treatment to students is clearly biased and incorrect. I just want to leave to you guys whether my answer was right or wrong, since I've just lost trust from my teacher.

Doesn't anyone care for change? Education is Important! We deserve a decent education! I have much to say, but are usually useless to say. Who cares about the future? Teachers are pure idiots, they don't purely do their jobs, they apparently don't value correctly education. youtube.com/watch?v=zDZFcDGpL4U
Can anyone help me with my question, because I'm filing a complain against that teacher?

Chord may or may not pass through the center of the circle so your argument is wrong.

You're wrong, the teacher's right.

Guess it's time to make your peace with your teacher. :)

In Geometry, all chords of a circle have exactly 2 points. A point is defined as being the position on the circumference of the circle where the line of the chord passes through. A chord that passes through the centre of a circle is its diameter.

A diameter is a chord, it is the longest chord, it has the definition of a chord. Therefore the diameter which meets 3 points and contains them, is included in the statement "every chord".

A line segment is a series of points, not just two endpoints. The center exists, because it is necessary for the definition of the radius, therefore FALSE.