@JustineBorzumat If you created groups that are just each student (I would have Canvas automatically create the same number or groups as you have students, or set it to create groups with 1 student in them) and then set the discussion to a "Group Discussion" this would create a private discussion between just the student and the teacher. Group discussions stay private to just the members of that group and if there is only one student in the group, you are essentially creating private discussions. Otherwise, a discussion is open to the entire course.
I am guessing you are wanting to have more back and forth, otherwise I would just create an assignment that has a text box entry and then the teacher can use the comment field in Speedgrade to comment back. This might get weird if you are wanting lots of back and forth though so see why the discussion might work better.
Hope this helps!