Thank heavens someone has brought this up. It's a problem I've had all my life, too. It's hereditary, I am sure - I remember my grandmother doing it. My nails have always been weak and brittle, too, so I have always been ashamed of my fingers (piano lessons, even as a adult, or bleeding on freshly washed laundry when ironing or folding it).
This goes through phases and sometimes my nails are fine and the cuticles aren't too badly butchered. Usually in the summer, nails and cuticles grow better and look better, but on 1st September, they start breaking off and deteriorating. I could set my watch by it!
This year, funnily enough, although we are well into September, I have suddenly got good, strong nails, and am trying really hard not to pick the cuticles. Not sure if this is due to hormones - I thought I was well past the menopause by now.
Haven't found the ultimate cure, but I do use nail oil and a hand-massage oil which I keep in the bathroom cupboard and beside my bed respectively. It has helped a little.
Keeping a pair of nail clippers really close at hand is also a better way of cutting off those snags, as you can do it so that there is nothing left to fiddle with. This is even more effective if you soak your fingertips first. I suppose there should be warnings about cutting too far into the cuticle, but I have never had any problems with that.
What I keep meaning to do is an old method I used to try in my teens which was to warm a small bowl of olive oil and soak my fingers in it, then cut off any threatening snaggy bits, then apply a thick layer of hand cream and cotton gloves. This just before bedtime - the warmth in bed then improves the effect.
Also apply a thick layer of hand cream under rubber gloves before washing up or cleaning with really hot water for the same effect.
The best cure must be some kind of psychological programming - telling yourself it's a disgusting habit or finding something else to fiddle with whenever you feel the urge.
As I've just noticed I'm doing it while reading through this post, obviously the very first step is to make yourself aware that you're doing it. If you're anything like me, you don't even notice it.
Good luck with breaking the habit. As an incentive, reward yourself with a nail care treatment when you've managed to get all 10 nails looking healthy and nice!