Why do hangnails hurt loads, and then feel great when you've properly got them out? I'm aware they can get infected, but I'm talking about in the short term.

I'll be giving it a wee chew, and then go too far and get a bit of nail near the skin, and it will cane, then throb for a bit. If I can get the last bit out, down to the root or whatever nails grow from, it's fine, throbbing disappears almost immediately, but otherwise it hurts.

Why is it better to rip my skin off than leave it forlornly hanging?