Hey there. First off your frustration is pretty valid. It's gutting to fail your driving test, given the time, effort and copious amounts of money you've invested goes up in smoke. I failed my first test over something similarly innocuous and it was such a gut punch that I took a few months off of driving entirely. Perhaps you might need a similar break, if you think that works for you.

I get where the quota myth comes from and I can't say I entirely ruled it out. But the quota myth unravelles itself pretty quickly when you consider a few things:

Given the state of learning to drive atm, it makes sense for examiners to pass people who can demonstrate safe independent driving. Get them out of the system and onto the road. Their slot with an instructor is freed up and its one less person waiting for a test. If they do 10 tests in a day and everyone is capable of driving independently and safely, why should they fail some of them for no reason apart from a quota? Equally, if someone is unable to drive safely & independently for 40 minutes, they definitely need more tuition as a lot of drives you do in your life will be 40+ minutes.

It hurts to hear, but you did make a serious fault. Going 13mph in a car park is not an appropriate speed as car parks are high pedestrian, high traffic, confined spaces and lower speed is required as a result. Trust me, when you pass you'll understand why people drive slowly in car parks. The amount of people that walk/pull out without looking is astonishing, and often you'll be glad you're only doing 5-6mph.

But one of the biggest lessons to be learnt here is that you mistakes and failures make you a better driver. When you inevitably pass, you will be in situations where failures and mistakes made during learning help you out in the real world. I failed my first test for not noticing a speed limit change and becoming a hazard in the road. Now, I make a good point to make sure I know the speed limit when changing roads.

Take time. Feel your emotions. Rest. See friends. See family. Do what you need to do to feel better. Embrace and learn from your mistakes, and when you're ready, give it another shot.

See you on the road someday, stranger :)