Source - YC partner.
Have a great idea, a great team, show some traction. Traction probably doesn't have to be revenue. Just find something that shows other people want what you're building. Great team means you're the best team for your idea. Not necessarily Ivy League school or Google/Facebook/Amazon employment.
Our founder split made them worried / didn't fit with their thesis. That seemed to be the only thing, based on our back and forth.
So, keep in mind that YC is looking for something very particular. It does strongly suggest however that YC is very open to taking teams they don't know as long as they fit their official and unofficial criteria. They make a serious effort to be transparent but they are also oberworked and are pretty much a black box to most startups they reject. They surely were for us, I just got lucky to get an answer.
When we make an accelerator, it'll also be based on a certain way of doing things. But it'll be very different. We believe that standardized platforms make a huge difference - YC has one as do other accelerators. But we have an actual software platform on which others can build their apps. It would be as if FB ran an accelerator program to develop new businesses on top of the FB platform. Our program could have actual measurable metrics to determine who is funded further and who is not.
Unfortunately at scale YC operates today (~2,500+ submissions per batch) this is no longer true. It's simply too difficult to get through all of that noise without "knowing someone", and the exceptions to that rule are getting rarer every batch.
Source - ask any YC Alumni candidly.