Yoga originally started as Guru Parampara tradition. This means a lineage in which each guru taught each disciple at a time and kept the tradition alive. Back in the day, there weren't classes full of students doing the same asana (postures) sequence. That is why I believe so much in a one-on-one session that will help each individual with their own needs.
Picture this: One day you feel very energetic and in need of a stronger practice with more flow. Another day you might feel you're coming down with a cold or had a busy week at work and you might need to take it easy. We're all different and we lead lives that most of the time do not allows us to stop. In doing a private class you can use all the knowledge in yoga to do a practice that will help you improve whatever condition you're in.
Not to mention that your body is unique and requires different things than the person next to you. Listening to your body and respecting what it's telling you is key in developing an even better yoga experience.