What you’re seeing makes sense, but I can see why it feels like an endless loop. On Apple’s side, your iCloud email address isn’t technically its own separate account — it’s considered an alias (or sometimes the “primary email”) of your Apple Account. That’s why in System Settings → Internet Accounts, macOS shows it tied to “iCloud” rather than letting you add it again as a standalone mail account. Essentially, macOS is preventing you from duplicating the same credentials twice.
Since it works on your iPhone and iPad, the good news is your Apple Account and iCloud Mail itself are healthy. The loop happens because Mail on the Mac is expecting you to enable the “Mail” service from the existing iCloud account, not create a brand-new Internet Account. Here’s what usually fixes it:
1. Go to System Settings → Internet Accounts
2. Select your iCloud account (the one showing your alias).
3. In the list of toggles (Mail, Contacts, Calendars, etc.), make sure Mail is turned ON.
4. Then open the Mail app, and your iCloud inbox should appear automatically.
If you already tried that and it still loops, sometimes removing the iCloud account completely from Internet Accounts, rebooting, and re-adding it resolves the confusion. Just be sure you know your Apple Account password and have two-factor authentication handy before signing out, since it will sign you out of other iCloud services on the Mac as well.