Gmail's POP3 configuration maybe sometimes confusing.
In the Gmail's web interface in "Settings" on "Forwarding and POP/IMAP" tab you can find a drop down list called "When messages are accessed with POP".
Here's the value list and the Gmail's behavior:
a.
"delete Gmail's copy":
Message is deleted by issuing RETR command.
b.
"keep Gmail's copy in the Inbox":
Message stays in the Inbox,
Web interface says it's unread, however message is not received
for the second time using POP3 client.
c.
"archive Gmail's copy":
Message is deleted by issuing RETR command, however it is
possible to find it using web interface.
Gmail simply ignores DELE command, and does not follow POP3 standard.