As David suggested this is likely scope related. Since ngRepeat creates a new scope your ngClick is setting the sortColumn and reverse in its own child scope for each column header.

One way around this to ensure you are modifying the values in the same scope would be to create a function on the scope and call that in your ngClick passing in the index:

$scope.toggleSort = function(index) {

    if($scope.sortColumn === $scope.headers[index]){

        $scope.reverse = !$scope.reverse;

    }                    

    $scope.sortColumn = $scope.headers[index];

}

with this as your markup:

<th ng-repeat=header in headers>

    <a ng-click=toggleSort($index)>{{ headers[$index] }}</a>

</th>

Here is a fiddle with an example.

Another option would be to bind to a non-primitive type like this (the child scopes will be accessing the same object):

$scope.columnSort = { sortColumn: 'col1', reverse: false };

with this as your markup:

<th ng-repeat=header in headers>

    <a ng-click=columnSort.sortColumn=headers[$index];columnSort.reverse=!columnSort.reverse>{{ headers[$index] }}</a>

</th>

Here is a fiddle with an example.