"But why is vi brought up whenever Emacs is discussed?"
Because emacs users and vim users are disjoint, despite having almost everything else in common!
because they're both awesome and we always want to know which one is awesomer!, now please lets not include TextMate in this conversation :)
I'm a VIM user and I always like the cool things Emacs users can do, even though I'll never use Emacs.
[1] Or rather, "empowers you to do"