In order to answer this you must first know the history of Missouri. I will tell you what I have learnt.
1. According to the Northwest Ordinance it prohibited any form of slavery.
2. Slavery is basically when you are a slave,a slave is a person that is controlled by another person; they are somebody else's property.
3. Nevertheless Missouri wanted to be a slave state.
4. A slave state, basically is a state that makes slavery legal.
5. Look back at point 1, Northwest Ordinance prohibited slavery.
6. Therefore, they would not allow Missouri to become a slave state.
7. That didn't mean that there weren't slave states though, there were.
8. 11 states were slave states, some are Delaware, Kentucky and Maryland.
Back to your question, let us first focus on what a free state is.
A free state is basically an independent state, a state that is not governed by any other state, just itself.
To sum, the Southern Congressmen didn't want Maine to enter as a free state because they wouldn't let Missouri be a slave state.
To let Maine be a free state you would have to let Missouri be a slave state.
