Sorry you weren't fully informed or read documentation on POP. It's not designed to work with subfolders so you will only ever be able to get messages in the Inbox.
I don't get why your friend suggested using a POP client. Doing so alone is not going to backup email messages. In fact, if you are indeed using Thunderbird, then you already have a way to backup messages to your notebook. You should have a "Local Folders" account. Like the name implies, these folders are on your notebook's disk - you can even change the directory. Just drag and drop messages or folders from the remote account's folders to the Local Folders account. I don't use a Mac, but you may have to hold the Cmd key? to perform a copy and paste instead of a cut and paste. Or at least on Windows Ctrl-drag will do a copy and paste.
And you can go a step farther and backup messages to a different mail server (using IMAP) by also using Thunderbird this way. There is a also a utility on DreamHost servers that you can run from shell that will copy or move messages between different accounts and local disk as well.
Thunderbird and many other clients also have a feature for saving messages locally so that you can access them when not connected to the Internet, without the need to manually copy them to a Local Folders account.