There are a whole myriad of reasons, and one person's choice will be for a reason completely different to another's.
For us (private secondary, although both went to state primary - although we took DC2 out for Y6 as it had been such a waste of a year for DC1 with constant sats focus):
DC2 has mild SEN, which wasn't managed at all in state school, having small class sizes has meant they've needed no additional assistance. He'd have been eaten alive at the local comp.
DC1 is quite bright, but because she wasn't one of the school's 'performers' she was constantly overlooked to primary. She's just done her GCSEs and come out with all 9s and 8s, so I guess she's flourished.
There is only one state school near us (live rurally), and sadly it seems to be a race to mediocrity, very little expectation or aspiration for the children. The catchment is very 'naice', but each year more and more parents are opting out of sending their kids there and choosing private. I've seen some fantastic success stories of bright children who've gone onto top tier universities , but sadly I've also seen too many with incredible potential just not have that potential fulfilled.
However, I know there are many amazing state schools - I don't believe one is better than the other, and it must be considered that private schools only account for 8% of the population, so the vast majority of doctors, lawyers, accountants etc, will still have been state educated. Having a private education does not mean you automatically fall into a well-paid profession, just as having a state education does not mean you won't, ultimately each individual needs to put the work in to get the outcome they hope to achieve.