how do passwords work?

newbie here. so consider this paradox: let's say you have a pass protected rar file. now the password should be stored somewhere in the file to compare against the inputted password. so if it's there how come you cant just extract it?

>>30
When I was younger I knew this wouldn't work. However! I was a clever bastard, and I XOR encrypted the resulting file (with only a 32-bit key) and compressed again. Instead of wasting space (at optimal compression), I was able to get another roughly 10%. Lather, rinse, repeat--even with the same key¹ the results continued to be favourable for as long as I cared to do it, which admittedly wasn't very long, for I was doing this with a 486 and each pass was taking longer and longer.

_________________________________________________________
1. Do you know the reason for this restriction?