The question has already been answered, so I'm just gonna make a brief remark: in your question, you use the terms "folder" and "directory" interchangeably. Those two are very different, and in my experience 99% of all problems with Unix permissions have to do with confusing the two. Remember: Unix has directories, not folders.
EDIT: a folder is two pieces of cardboard glued together, that contain files. So, a folder is a container, it actually physically contains the files it holds. So, obviously a file can only be in one container at a time. To rename a file, you not only need access to the folder, you also need access to the file. Same to delete a file.
A directory, OTOH, is itself a file. [This is, in fact, exactly how directories were implemented in older Unix filesystems: just regular files with a special flag, you could even open them up in an editor and change them.] It contains a list of mappings from name to location (think phone directory, or a large warehouse). [In Unix, these mappings are called links or hardlinks.] Since the directory only contains the names of the files, not the files themselves, the same file can be present in multiple directories under different names. To change the name of a file (or more precisely to change a name of a file, since it can have more than one), you only need write access to the directory, not the file. Same to delete a file. Well, actually, you can't delete a file, you can only delete an entry in the directory – there could still be other entries in other directories pointing to that file. [That's why the syscall/library function to delete a file is called unlink
and not delete
: because you just remove the link, not the file itself; the file gets automatically "garbage collected" if there are no more links pointing to it.]
That's why I believe the folder metaphor for Unix directories is wrong, and even dangerous. The number one security question on one of the Unix mailinglists I'm on, is "Why can A delete B's files, even though he doesn't have write access to them?" and the answer is, he only needs write access to the directory. So, because of the folder metaphor, people think that their files are safe, even if they are not. With the directory metaphor, it would be much easier to explain what's going on: if I want to delete you from my phonebook, I don't have to hunt you down and kill you, I just need a pencil!