Having a fresh perspective when working on solutions to your problems makes all the difference. Albert Einstein said: "Problems cannot be solved at the same level of awareness that created them."
When I coach, I become that person that can give my clients a fresh perspective and guide them more quickly to solving their problems. They were stuck on their own for a long time because they were still in the "problem awareness."
When clients and students start in my programs, as their coach I am already in the "solution awareness" for solving their problems. This always works really well for our coaching sessions, and I hear this a lot from them: "Wow, I did not think of that" or "Wow, I never saw it that way."