I have cysts on my back my doctor is reluctant to take them out due to scarring, can they be drained medically?

Epidermal cysts can be drained but they may reform. Particularly if they become infected then draining them by making an incision (cut) in the cyst is usually the best treatment. Once the infection has resolved and the area has healed consideration should be given to surgically removing the area to prevent the cyst recurring. Recurrence is particularly likely if their is still a lump or residual cyst.Best wishes.

The only way of completely resolving the cysts is by surgically removing them.  If someone open them and evacuate the content it will lead to fibrosis, scarring and the recurrence of the cyst.