Writing is self-taught. You learn to write by doing it, not by listening to somebody tell you about it. Writing is a process. Writing grows and changes over time, but sometimes the earlier stages of writing are not incorporated into a course where the teacher and students must cover a certain amount of material. Seeing a consultant at several points while doing a paper means that the writer begins work early and gives ideas time to develop, rather than jamming the entire composing process into one marathon session the night before the due date.
Writing is social.
Peer consultants are ideal readers, because they can explain where they get lost, where they become bored or frustrated, what they want to hear more about. They can also check the assignment and make sure the draft meets all specifications. Because writers understand their own ideas perfectly, they assume the ideas have been transmitted to paper, even when they haven't. Writing is self-taught. Sessions like this are hard work for writers, so they teach themselves more than students who try to produce a paper alone.