cp -L vs. cp -H

With symlinks, tools have two things they can do:

1. Treat the symlink as a symlink ("preserving its nature"), or
2. Treat the symlink as the type of file that it points to.

Saying that -H "preserves its nature" is not a contradiction. Consider the alternative. If you use -L, any symlinks cp finds will be opened, and their contents copied to the target file name. So the source was a symlink, but its copy is not a symlink. So it "lost its nature as a symlink".

Consider

$ mkdir subdir
$ echo "some contents" > subdir/file
$ ln -s file subdir/link

# definition of "list", the abbreviated ls -l output used below
$ list() { ls -l "$@" | \
    awk '$0 !~ /^total/ { printf "%s %s\t%s %s %s\n", $1, $5, $9, $10, $11 }' ; }

$ list subdir
-rw-rw-r-- 14   file  
lrwxrwxrwx 4    link -> file

$ cp -rH subdir subdir-with-H
$ list subdir-with-H
-rw-rw-r-- 14   file  
lrwxrwxrwx 4    link -> file

$ cp -rL subdir subdir-with-L
$ list subdir-with-L
-rw-rw-r-- 14   file  
-rw-rw-r-- 14   link  

The difference in behavior between -L and -H comes when -r is specified as well. cp won't create symlinks in subdirectories with -L -r but it will if you use -H -r.