My doctor wants me to discontinue Finasteride and restart after 6 months. How can I convince my doctor to prescribe it?

DO NOT STOP finesteride, if you have regrowth you need to continue or it will all fall out.  start growth factors (see link), roller, vitamins, rogaine and do PRP/acell in the office.
I suggest a formal consultation as there are a combination of treatments that can be done to improve har loss.  Oral finesteride has very little to no side effects in the majority of people; PRP/platelet-rich plasma + stem cells like A Cell help regrow hair and slow down the thinning process; rogaine and restorsea spray should be used daily; oral viviscal helps keep nutrients high in the follices as well.  Transplantation is a last resort but works early in the aging process as well.  A formal consultation and combination treatment is needed.  Best, Dr. Emer. 

In  my opinion, if you do not have adverse side effects from finasteride, there is no reason to discontinue it. Taking a 6-month break may affect the positive results you have obtained. 
Jeff Rapaport MD FAAD
Realself Verified All-star

Great question. Well, this is a frequent question, I understand and respect your doctor's opinion but If you are having great results and NO side effects then I won't recommend to discontinue the medication. You always have the option of a 2nd doctor's opinion. Good luck. 

I totally agree with you, stopping finasteride would bring back your hair loss plus what you would have lost over the time you took it,  In other words, stopping might leave you worse off than when you started it.  Your doctor is wrong