Explanation:

- Some parents are not in favor of a co-educational system.

- The correct word is "favor." It means to support or approve of something.

- Some parents are not in side of a co-educational system.

- "Side" is not used in this context. It would need to be paired with "on the side of" instead.

- Some parents are not in thinking of a co-educational system.

- "Thinking" is about the process of thought and doesn't fit well here.

- Some parents are not in prefer of a co-educational system.

- "Prefer" needs a different sentence structure, like "prefer a different system."

- Some parents are not in judgement of a co-educational system.

- "Judgement" doesn't fit as it implies making a decision or assessment.