My left index finger has something similar. It was the result of something being jammed deeply into the cuticle. (Edit: Jewelers screwdriver, and yes I was misusing that tool at the time) I suspect a bit of scar tissue is mucking things up.

My nail is just a bit thin, from the underside, and if the nail gets too long, it tends to split and tear off to the short side, leaving a big chunk missing.

I asked my Doc about it once, About the only option is to remove the nail. Anything else would likely just make the problem worse.