If you are using a local account named administrator, and uses a Microsoft account login in. At this moment, windows 10 will binding your Microsoft account and administrator, and the option “Sign in with a local account instead” is disappear.
For this situation, Delete account represented as a key in registry from the following location:
HKEY_USERS.DEFAULT\Software\Microsoft\IdentityCRL\StoredIdentities
After delete, restart computer and test again.
Of course, you could create a new local admin account by Computer Management\Local Users and Groups\Users\New Users
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