I accidentally signed up for 2 step verification and now I cannot get into my Gmail account on my MacBook using Mail.app. I don't have a phone where I can access emails so this is all confusing.
Here it is explained how to turn off 2-step verification. If you don't have a mobile app or a mobile phone for verification, you should have received temporary codes. If you did not save them, well, then just follow the link below the login box where it says "Can't access your account?".
The "correct" way of accessing your Gmail in this scenario, is to create app-specific passwords:
App passwords allow 2-Step Verification users to access their Google Accounts through apps such as Mail on an iPhone or Mac, or Outlook. We'll generate the app passwords for you, and you won't need to remember them.
You will generate one password per client, e.g. Mac Mail. When Mac Mail is setup to use this password, you can fetch your mail just as if you hadn't enabled 2-factor authentication.
The app-specific password only gives access to fetch/send mail, not to other aspects of your account, so you will still use 2-factor authentication for logging in via Gmail's web interface.
Also, the password can be easily revoked, without affecting your account passwords or other app-specific passwords.
If you don't have phone, you can use the backup codes if you noted it already, else select
Can't access your account ?
Select I can't access my phone and backup code
Fill the form and wait for 2-3 days