Your emails are not "deleted" when you read them, they simply become "read" and logically disappear from the unread folder.
If you need to see your inbox rather than the unread emails, tap the [Edit] alongside the Mailboxes header and select the inbox of the mail account(s) you want to show. If you deselect the [Unread] you will still see the unread mail items in each of the inbox folders.