If you're interested in the culture
Native speakers do more than just teach you grammar rules and new vocabulary. They also introduce you to their culture, mentality and way of living. So in addition to studying a foreign language, you'll also get a chance to learn of new traditions and customs. It's especially great for those who travel a lot and like to meet new people. Just make sure to take lessons with someone from a country that you're truly interested in.
If you want to learn how to think in a foreign language
When we talk about lessons with native speakers, we usually mean the communicative approach that most of them use. This method works great for people whose goal is to learn not only to speak, but also to think in a foreign language. So if you want to express your thoughts freely without having to translate them from your native language first, you should consider studying with an English or American tutor.
If you want to overcome language barriers
Being afraid of speaking and making mistakes is something that most learners face, regardless of their level. You can only deal with it if you get as much practice as possible. The best way to achieve that is by studying with an English tutor. In that case you won't be tempted to use any other language. Of course it will still take some time to get rid of any shyness that you might be having. But you'll soon have the opportunity to make sure that talking with native speakers is not nearly as hard and scary as it sounds.