Should I report my father for using my social to take out cable accounts in my name?
That's bold. Where do you think your father may have got a hold on your social?
I believe my mom may have stolen it from me and told my dad about social media account.
If it's okay to report your parent's wrong doing to authorities. By doing that it will deter them from doing the same thing in the future.
I want someone teach my father a lesson. He stole from me and I want to make sure he won't do it again.
Well if you do report, he might learn the lesson. He shouldn't have stolen your identity like that. It will cause you a lot of problems.