He wants to create a backup of just the incoming email (that he has received) and skip archiving the Outgoing email that's in the GMail Sent Items folder.
Very interesting question and fortunately, there's a simple workaround as well - just follow these steps: [Gmail won't download items in Trash and we'll use that feature to our advantage here]
Step A: Clear all message from the GMail Trash folder by selecting "Empty Trash Now"
Step B: Open the Sent Mails folder and choose Select All. You'll now see a new link saying "Select all n conversations in Sent Mail" - Click that.
Step C: Select the "More Actions" drop-down and apply a new unique label like "WorkUnderProgress"
Step D: Select the "More Actions" drop-down again and choose Delete action this time [Don't be scared, logically we are just moving email from one folder to another]
Step E: Start Microsoft Outlook (or Thunderbird or Apple Mail), setup the POP configuration and start downloading your GMail locally. The items in Trash section of your GMail account won't be downloaded.
Step F: Once the download is complete, goto the GMail Trash folder and select all messages. Click the "Move to Inbox" button (be careful not to press the Delete Forever which is just next)
Step G: Goto the WorkUnderProgress folder, select all messages and click the Archive Button. Then from the drop down, choose Remove Label - WorkUnderProgress.
Congratulations. You are done. Here are some related GMail Tips & Tricks that might interest you as well:
Move GMail Messages from One Account to Another
Is Your GMail Inbox Full ? How to Clear Inbox Quickly