I want to know if there is any distinction between care and care about. For instance, I often say 'What do I care about?' rather than 'What do I care?'. I looked up the Merriam-Webster dictionary and it did not help. It seems care and care about are almost the same. Sure I know in care about, care is an intransitive verb.
My possibly wrong guess is that care about puts more emphasis on the object that we care while care is very much focused on the verb itself.
'What do I care about' is really weird like you guys said. It should be 'What does somebody else care about?'. My bad :).