It means he really doesn't want to talk to you or people who are like you (similar to you). He doesn't like your character, or the way you behave, etc. So it is like saying: I will be talking / answering to you AFTER my death only (in other words, NEVER)

i will die, you can kill me and i still will not answer to a person like you answer to - give reasons for doing something so it means, i will not give you an answer because you are not important enough for me to need to

I think there are 3 parts to your question. I'll be dead before", implies you will never do something or something will never happen. "Answer to", means you will take orders or explain your actions to someone. "To the likes of you", implies somebody you do not respect for whatever reason in that context. So in total, "I will never explain my actions or take orders from you because I don't respect you" I'm sure there will be others who will be able to give a better technical definition.