Earlier quoted context omitted.
This follow-up shows a lot of maturity. Both sides are obviously at fault here, although you instigated it. I suspect you could still get the internship if you send an apology like "Sorry for my previous emails they were out of line. You're essentially correct and here's an updated resume to reflect that."
Thank you - I actually did send an apology email, but since I'm pretty sure I'm not quite qualified for the position, I didn't bother pursuing it any further than that.
If so, that's really really sad. Even more so if you thought "Unix-like" genuinely disqualifies you because it's not strictly "Unix" !
You need to be more confident about your skills. Most interns don't know how POSIX relates to UNIX and Linux like you do, if they are even familiar with the word !
Look, I'm a former Facebook production engineer. I won't exactly reveal a secret by saying that FB is wholly Linux based. It's not a bank with legacy commercial Unix systems, and you were of course right about the 1970s engineers comment.
Positions requiring expertise with a specific brand of Unix are less and less common, and these would always mention the flavor they're after anyway (mostly Solaris, possibly some AIX/HP-UX).
One more general piece of advice : let others decide that you're not qualified for, don't self-censor before you even get a chance to fight.