Why should you care about yourself... specific reasons may have to be from you. General reasons...
concrete: because everyone (other than the obvious people) has value and deserves to be cared about.
abstracts and potentialities: Someone in the future may really need you... may need help and support and you may be the best qualified for that.
Somewhere in the future there may be an animal that will need rescuing... and you're the person who will do that.
Somewhere a man (or woman) may be waiting for that certain person who is their soulmate.
You do care but it's all twisted up inside and needs to find its way out. Give it that chance.