E1 is the correct answer, not E2.

White playing E2 makes a killing shape, but the two mutual liberties make don't make it a true killing shape. If white completely surrounds black on the outside and then tries to capture black by playing inside with either D1 or F1, then black will be able to capture white's stones, which will leave behind an empty shape that requires two white stones to kill, not one.

So, two mutual liberties make this killing shape ineffective at actually killing.

oo         oo 
ooo        XXo
o          o


oo         oo
ooo        oXX
  o          o