Use rbenv
to setup a ruby binary that is in your home dir (a writable path).
You get that error because you lack write permissions to the System dir. Don't try to get write perms there - that's just asking for trouble. Instead, install a ruby version manager.
rbenv
is linked above. Some like RVM. You can google for the arguments that pro/con each. rbenv
is "more unix-like" and that is a good reason on its own.