Apple and Google can be described as frenemies. They both need each other to a degree though Apple needs Google far less. But when you are a Mac OS X or iOS user sometimes there are a few “quirks” with using certain Google services.
One such annoyance I had been having was some of my new Gmail messages were immediately going to my archive folder in Apple Mail. I knew this because I could read them on my iPhone and iPad but then they were MIA on my Apple Mail inbox on my Mac Pro.
Here is the solution:
Click on settings which can be found here. It is the gear wheel icon in the upper right corner.
On the next screen you should see something like this. Click the LABELS tab. Then scroll down to the ALL MAIL setting an UNCHECK show in iMAP. Once this is done you will no longer have archive folders within Apple Mail which gets confusing and causes the missing emails to go there at times.
You can now log out of Gmail in your browser. The final step will also likely fix the incessant and non-stop incoming mail messages issue where under your mail activity it never stops showing incoming mail messages. These are the Google recommended settings for iMAP and Apple Mail
Inside Apple Mail open preferences. Select ACCOUNTS then select MAILBOX BEHAVIORS tab. Choose the following settings which are recommended by Google for IMAP and Apple Mail. You should now no longer see the constant incoming new mail message under mail Activity panel.