mac os x / icloud login just freezes

Only iCloud keychain is corrupted , not the login keychain .

If keychain access is opened and also its preferences , clicking on reset my default keychain will reset both login keychain and iCloud Keychain and you will loose all passwords saved .

If iCloud Keychain is corrupted in Mac .

( a ) Use an iPhone and sign in with same Apple ID and password in your Mac .

( b ) In iPhone go to settings , iCloud open keychain and click on advanced two options will be shown reset code and reset iCloud Keychain , click on reset iCloud Keychain .

( c ) A verification code will appear on your mobile number through sms and it will prompt to generate a code , think of code and fill up in the field so keychain will be set up in iPhone , write down this code .

( d ) Come to Mac in system preferences > click on iCloud the box of keychain is unchecked , so tap the keychain box , it will show waiting for approval click on option button , enter the passcode that is generated in iPhone , click on confirm .

( e ) Again in iPhone a pop up will appear showing approve or deny for name of Mac to approve for keychain , click on allow .

( f ) In Mac click on option button enter trusted number an sms will come having a verification code , enter it the trusted number will be saved and visible and finally keychain is set in Mac .

See the article If iCloud Keychain won't turn on or sync - Apple Support

Set up iCloud Keychain - Apple Support