Voce pode ter dado permissão de escrita, mas o próprio sistema de arquivos do seu HD externo esta montado como "somente leitura" (ro).
Alguns HDs externos, possuem uma "chave de segurança", veja se o seu tem essa função.
Tente o comando:
mount -o remount,rw
-o Options are specified with a -o flag followed by a comma separated string of options.
-w Mount the filesystem read/write. This is the default. A synonym is -o rw
remount
Attempt to remount an already-mounted filesystem. This is commonly used to change the mount flags
for a filesystem, especially to make a readonly filesystem writeable. It does not change device or
mount point.
The remount functionality follows the standard way how the mount command works with options from
fstab. It means the mount command doesn't read fstab (or mtab) only when a device and dir are
fully specified.
mount -o remount,rw /dev/foo /dir
After this call all old mount options are replaced and arbitrary stuff from fstab is ignored,
except the loop= option which is internally generated and maintained by the mount command.
mount -o remount,rw /dir
After this call mount reads fstab (or mtab) and merges these options with options from command
line ( -o ).
ro Mount the filesystem read-only.
rw Mount the filesystem read-write.
Veja o man do mount: # man mount