This is an old thread but I thought I'd post an update here because I think there's more than one cause for this issue and problems with Outlook seem to come and go regularly (and are different on a Mac and a PC, by the way).
- Recent versions of Outlook no longer seem to accept account usernames that are not email addresses. There are still many old accounts out there that have simple text usernames - if they can't be changed, or won't accept an '@' character or periods then you can't use Outlook.
- Recent versions of Outlook don't allow you to set advanced settings until the initial automatic setup attempt fails. Since the initial setup process typically guesses the servername based on the user's email address and that will often fail for an address that uses a personal domain (different from the mail server name) that means you have to accept a "certificate mismatch" security warning before you can configure the account correctly.
- Recent versions of Outlook won't work with an account name that is different from the "from" address that messages are sent from. That means if you want to forward incoming personal mail to Gmail (for storage, spam filtering and mobile access) but reply from your personal domain, you must first set up the account in Outlook for the outgoing domain, then reconfigure the incoming server settings. This is a bit counter-intuitive.
- Recent versions of Outlook wouldn't allow you to set up the account for a personal domain then change the incoming server to Gmail. This seems to have been a bug that has now been fixed at least in the Windows version. One workaround was to move all mail to live.com but I had big problems there with spam filters silently discarding wanted emails so I no longer recommend that.
- Outlook tries to use port 465 (which has been deprecated for years) instead of port 587 for outgoing encrypted connections, which sometimes causes connections to fail.
- Gmail often blocks Outlook passwords even if "Allow insecure applications" is set in Gmail settings (and even after initially accepting the password). The solution is to use an "App password" for connection to Gmail, which is only possible if you have enabled two-factor authentication in Gmail, which is only possible if you have a mobile phone.
All of these things can (in my experience) cause very similar symptoms to the authentication problems discussed here. The solution is to get an experienced person to sort them out for you, or try a different client (many people now seem to use Thunderbird, a web browser or a phone app if they can - they tend to use Outlook only at work, connected to Exchange and managed by someone else).