I feel like tutoring is a combination of coaching and teaching. When you're tutoring a student, you begin by teaching content: you either teach the student a new concept, or review something they might have already covered at school.
Then coaching comes in. You will give the student problems they struggle with, but as the coach you have to sit back and allow them to struggle so they can learn the concept. Think about athletic coaches, like Andy Roddick's tennis coach. Do you think when Andy is at practice and struggles or makes a mistake, his coach jumps in and shows him how to do it? No. He might verbally give him tips, but he never jumps in, takes the racket, and shows him exactly how to do it.
Tutoring is the same. We need to give students a chance before we jump in and help. They need to learn independence and build confidence because when they sit down to take a test and struggle with a problem, we won't be there to jump in and help them. They need to show confidence in themselves and their knowledge so they can tackle the challenging problems they come across.
After a tutoring session, I want my student to feel like they learned something new, useful and relevant. I want them to feel energized and excited about what they learned. If they get frustrated, I want them to know that if they keep working at it, they WILL eventually "get" it and succeed. I don't want to give the student all the answers or be their crutch. I want to teach them strategies and ways to approach their work that will ultimately help them be successful when I'm not there.
Similarly, as a coach, you want to give your players the strategies, practice and skills to be strong players. You want your players to love the game, but you also don't want them to give up when things get tough. You know you can't play a game for a player - you need to teach them how to successfully play the game on their own.
A coach is a fundamental to the success of a sports team. They help organize the team, encourage and motivate the players, and create systems and strategies to help them succeed. An academic tutor is very similar. Instead of helping with a sport, a tutor helps students succeed in school. An outside person providing students with strategies, encouragement, and organization when necessary can really help them succeed! When you think about sports coaches, there isn't a question in your mind about how much they help. Why would it be any different for academics?