As Writing Center tutors, we learn from our tutees while we try to better their writing. The Writing Center is a diverse environment where people of all different backgrounds interact as they collaborate on the writing process.
While you may know everything there is to know about comma splices and their proper uses, your student may have a stronger authorial voice in their academic paper that you envy. As you work together, information is exchanged between the two parties, resulting in improved writing on both sides.
For me, I'm worried that I may not know every answer to someone's questions. So, I see the tutoring session resembling a volleyball game. Each participant contributes to the conversation, building off what the other's prior statement added to the discussion. In instances where you don't know the exact answer, you can either utilize resources that will find what you're looking for, or you can use personal experiences to provide examples. When in doubt, resort back to what you know.
Through this mindset of tutoring, we can become third-party observers for the student and their writing. We can introduce new perspectives for them to consider with their argument. Parts of the writing that are confusing or awkwardly worded can be brought to their attention through a fresh set of eyes. Writing Center tutors can be that supportive colleague who's going to tell you how it is but work with you to make your writing better.