It is like living alone or living with a partner. There are benefits & disadvantages of living alone & there are benefits & disadvantages in living with a partner. If you decide to live with your partner, things will not always be your way, you have to put in consideration the thoughts & feelings of your partner. If you decide to live alone, things can be your way, but then you will lose the benefits of living with a partner.
When you join a Martial Arts class, you are becoming a part of a team, things cannot be your way, you will be guided towards the development of the class as a whole, you will be a student, but you will also be a teacher for those who join after you. When you decide to take private lessons in Martial Arts, then teachings can be adapted towards your own individual goals. You will primarily be the student; you do not have to worry about anybody else’s growth other than your own.
Obviously private lessons will cost more than classes, as you are asking for the undivided attention of the teacher. Just like living alone opposed to living with a partner. If you live alone, you are responsible for all living expenses. If you live with a partner, you can split the expenses. There are benefits to both paths, but you have to decide which path is right for you. The teacher can help you decide, but ultimately, the decision is up to you.