Here's my reason for going private:
CROWDS.
This is the point where I decided to join a private golf club........................ Fundamentally, I was growing very tired of the waiting times and crowds at public courses. This is a recurring problem at many public courses in my area - they will not make tee times for singles, and it's very common to wait 1-2 hours for an available slot as a "walk-on". Even If you call ahead of time, the proshop insists on telling you on the phone the course is open, no tournaments, and it's easy to walk-on. LIES!
I went to a local course called "Westridge GC" to walk-on as a single. I was told to standby on the practice green, and they should have an opening in 30-45 minutes. TWO HOURS later, I still never got the call. The Proshop apologized, then immediately sent me to the #10 teebox (the course was starting on #10 that day, which is a long cart ride away from the clubhouse). To add to the confusion, there were no carts available, and I had to wait another 2-3 minutes for a cart. Once I (finally) got to the teebox, the Starter, and all the other golfers waiting to tee off were FUMING at me for my tardiness. There must have been 7-8 golfers all standing around the teebox waiting for me.
I had to explain that the Proshop directed me out there, to pair up with a 3-some on the teebox! Without a warmup, I immediately came under the ball, and put a huge Skymark on my BRAND NEW Titleist 980F 3Wood.

The ball popped up high, and only about 50 yards away from the teebox! As you would imagine, the starter, and all the golfers waiting looked at me as if I was a prize idiot.
PRECISELY at that moment, I made the decision to join a Private Golf club. I've never looked back since. Having the ability to make a tee time as a single golfer has changed my golfing life for the better.
I'll never go back to Public golf again, if I can help it.
As far as costs - Yes, it's less expensive to play public golf, especially if you can play during the week with coupons and special deals. Unfortunately - my work schedule only allows evening/weekend golf, so I can't do that, and have to suffer with the maddening crowds in my area.
As far as playing the same course - I also previously enjoyed playing multiple courses. However - I do not get bored playing the same course time and again - the teeboxes change, weather conditions are different, tees are moved around, pins/flagsticks vary, and my playing partners are always different. I don't mind it at all, but I do play with public golfer friends about 1 time/month for a little diversity.