I would never ever ever want my dad to give up on me. Teenagers will test their parents love. Just because she says things that are disrespectful does not mean she wants you to stop trying. But you also have to give her time (lots of time ) and space to heal. Keep showing her, through actions (but maybe also through words if that is her love language) that you love her dearly and want to be a good dad. With NO expectations in return. She may yell you to bugger off 100 times in a row. That does not mean she really wants you to. Love her unconditionally. Be the stable grownup that she needs.
And ghost, please please find some professional help for your self defeating thoughts and anxiety. I've been there. I know how impossible things can feel. But it may be the most important GAL activity you do.
I feel like you are in a dynamic here where you keep spinning in circles, folks use a stern tone and say you are not listening, and that only fuels your low self-image, as if we are proving your ideas about yourself.
But it is frustrating to see someone who is not willing to help himself. Be kind to yourself by being willing to get some professional outside help. Things CAN change for you if you are willing to give it a go.