Overall explanation Correct option:

Instance might be part of Auto Scaling Group and hence re-launched similar instance - Auto Scaling groups can be configured to launch an instance to replace an instance that is undergoing maintenance. This could have been the reason why an instance of the same type got launched automatically. The size of an Auto Scaling group depends on the number of instances that you set as the desired capacity. If you wish to terminate an instance that is part of Auto Scaling Group, the configuration of the group should be changed to a reduced number of instances, so the automatic launch of instances does not happen when an unwanted instance is terminated.

Incorrect options:

The user did not have the right permissions to shutdown the instance. User needs root permissions to terminate an instance - This is an incorrect statement. If the user does not have enough permissions, then the action itself is unavailable for him. A user does not need root permissions to terminate an EC2 instance.

The instance could have been a part of the Application Load Balancer and hence was automatically started - Application Load Balancer is used to balance the incoming traffic requests equally among the available EC2 instances so keep the performance and availability at its best. ALBs are configured with Auto Scaling Groups, but this is not specified in the use-case. In the absence of Auto Scaling Group, ALB cannot launch instances by itself.

The instance could have been a part of Network Load Balancer and hence was automatically started - As explained above for ALB, a Network Load Balancer is not capable of launching instances by itself if it's not configured with an Auto Scaling Group.