Well since earning respect is so hard, you can choose to talk it out. If that doesn't work,
"pretend to apologize, because you hate them but you don't want conflict ." If they don't accept your apology then forget about him/her because she/he clearly doesn't care enough about you to resolve the conflict.
AND THEN AFTER MAKE THEM EARN YOUR RESPECT, BECUASE RESPECT MUST BE SO HARD TO EARN IF YOU HAD SOMETHING TO DO WITH THE CONFLICT AS WELL.