Why does Drush require sudo?
I'd suggest you follow the official install instructions here after removing your current install - http://docs.drush.org/en/master/install/

When you have it installed then navigate to your home folder:

cd ~/
ls -lash


At this point your .drush folder should have your user as owner (not root)

If it doesn't then run

sudo chown myusergoeshere:myusergoeshere .drush -R


You can run ls -lash again and confirm the right user and group.

You should now be able to run drush without using sudo.



The reason you get that error is because when you installed it the system created the folder using the root user in your home directory so as your user you don't have permission to modify the folder.