Why is this simple AngularJS ng-show not working?

You need to tell angular that you updated the var:

function TestCtrl($scope) {
    $scope.loading = true;
    setTimeout(function () {
        $scope.$apply(function(){
            $scope.loading = false;
        });
    }, 1000);
}

or just

function TestCtrl($scope, $timeout) {
    $scope.loading = true;
    $timeout(function () {
        $scope.loading = false;
    }, 1000);
}