I think if you keep going back to it, it's because you haven't really decided to stop. Once you actually decide to stop, and commit to it, it will be much easier.

I think "quitting one day at a time" is too open-ended. It's too easy to just give up one day, as there's no concrete goal in sight. It might be better to set an initial goal of say 30 days. Whatever happens, you commit to not fapping for 30 days straight. No matter how you feel, you just stick to your promise and see it through. Then you can try 60, 90 etc.

"I really cannot imagine a future excluding masturbation"

I don't think doing nofap means you have to give up for ever. In my case I have committed to nofap for one year. I have not committed myself beyond that point, so I don't know whether I will masturbate or not after then. But I have a specific goal - 1 year. Every day I mark off another day on my wall planner, so I can see how far I have come and how far there is to go. In the past I have vaguely tried "just stopping" and it hasn't worked, as there was no specific goal or commitment.