Ask HN: Why am I blowing my interviews at great companies in the Bay Area?

I'm an iOS developer in the Bay Area with 8+ years of iOS experience (and 10 years overall) with a CS degree (non-ivy league, not Stanford). I've never had trouble finding work in the Bay Area, but my career has mostly been small, young startups and contract gigs. Lately I've been trying to find work at more established "Big 5"/FANG companies. Unfortunately it seems like I'm blowing my interviews and can't figure out what it is that they're seeing or not seeing in me. I've done two on-site interviews in the last 2 weeks, both of which went exceptionally well from my perspective. One was at Apple, the other at a very well funded and established startup with many ex-Apple/Google employees. I was invited for the on-sites after passing 2 phone interviews in both cases. Both on-sites were flawless from a technical perspective. I answered every question and solved every problem that was thrown at me. In both cases I met the hiring manager and VP at the end (so the interview wasn’t terminated early). And yet both rejected me without any explanation other than "we chose another candidate". I can't pinpoint what might have gone wrong. Is it an age bias (I'm in my late 30's) or perhaps over qualification for IC developer roles? Is it that these companies will only hire Stanford grads or candidates who have worked at other elite companies? Can someone tell me what other factors a hiring manager at an Apple/Google type company might be looking for, other than technical competence? Note that I have no trouble getting into smaller startups and also very lucrative contract gigs, but it seems like there's something preventing me from getting into the truly elite companies. I can't figure out what I'm saying or doing wrong. thanks!