So i think your problem lies in this bit of code.
$scope.items.push(key);
You continually use .push to add items to your $scope.items array. If your $scope.items array is only meant to show one item you need to re-initialize it inside your select_item function to clear it out.
So you should be able to do
$scope.select_item = function(key) {
$scope.items = [];
$scope.items.push(key);
}