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I haven't masturbated for about a year now because nothing really turns me on, men, women, animals, anything. It's nice because no awkward erections in public, but it doesn't seem normal.
In most people, even including most asexuals, orgasms are a natural function that even if they simply didn't do it, it would become uncomforting similar to having to piss, and would eventually happen on its own.
I tried an experiment a few years ago to see how long I could go without jacking off. After about a week it just happened on it's own. I also became extremely irritable and it was not enjoyable.
I'm going to guess you have a medical condition causing this, because even asexual's normally masturbate as a basic bodily function.