I am trying to use the alternatives system on CentOS Linux release 7.3.1611 (Core). I am trying to choose between multiple editors. I am following the tutorial here.
alternatives command (man page) is a tool to create, remove, maintain and display information about the symbolic links comprising the alternatives system. So, you make system-wide changes with it and, thus, you need a user with elevated privileges. You either have to
sudo update-alternatives (if sudo is installed and the user is a sudoer) or login as root with
su - and then run said command. This answer to a question about how one runs commands that need root permissions may be helpful to you.