Because [] !== false. You can coerce the length value to boolean instead with !!.

<div ng-hide="!!emptyArray.length">emptyArray is falsy, so do not hide this.</div>
<div ng-show="!!!emptyArray.length">!emptyArray is truthy, so show this.</div>

Edited:

AngularJS's directive hide or show depends on the function toBoolean() for evaluating the value passed in. Here is the source code of toBoolean():

function toBoolean(value) {
  if (value && value.length !== 0) {
    var v = lowercase("" + value);
    value = !(v == 'f' || v == '0' || v == 'false' || v == 'no' || v == 'n' || v == '[]');
  } else {
    value = false;
  }
  return value;
}

And you can verify the following code in JS console:

>var emptyArray = [];
>toBoolean(emptyArray)
false
>toBoolean(!emptyArray)
false

That explains why. Since when emptyArray is passed to the toBoolean() directly, it evaluates the correct result false. However when !emptyArray is passed to toBoolean(), it doesn't evaluate to true since !emptyArray is false itself.

Hope it helps.