How do I get rid of the stupid .me account that magically appeared in my Mac Mail on day?

Any @mac.com or @me.com email addresses are nothing more than aliases to you @icloud.com inbox. And they have been so since the fall of 2012. Neither is an actual email account any longer. They are just aliases to your iCloud email. The only account you have with Apple now is your iCloud account.

See this document -> iCloud: About your @icloud.com, @me.com, and @mac.com email addresses - Apple Support

To change the default “sent from” address for your iCloud email account, login into iCloud in a web browser and access settings there -> Use email aliases on iCloud.com - Apple Support

Try Mail/Preferences/Composing/Send new messages from and set it to a different account.

But you had to have created a MobileMe account in order to have kept your @mac.com address as an active address. So while you don’t remember it, you did indeed make a @me.com address if you have today a useable @mac.com address. MobileMe replaced the @mac.com email service ages ago, and iCloud replaced MobileMe in 2012. The only way anyone has a useable @mac.com address now is that they migrated to MobileMe when it came out, and then in turn migrated both @mac.com and @me.com to iCloud before the autumn of 2012 (not sure when .Mac went dead and you had to move to MobileMe, but it was somewhere around 2007/2008).

I provided the links to the support documents to manage the aliases to your iCloud account. But those old Apple email addresses are nothing more than aliases to your iCloud email account, and you need to manage them as aliases. They are not actual email accounts. They are just aliases to your iCloud email inbox.