Unless you're working on private data, is it such a problem to let Cursor train on your data?
I personally work mostly on small, unoriginal projects. I don't really mind letting Cursor keep the data for training if it leads to a better product for me.
It's not a problem for you maybe, but if you run a business providing some niche specific software in some area, having the model suck up all your code and learn from it is pretty harmful because your competitors and customers will be able to vibe code your product after the next model release. You're training a competitor to your business. People are very worried about this which is why companies like Claude don't train on enterprise data, and for lots of companies this exact situation is a deal breaker.
I often do reverse engineering work.
I find the idea of all the AI tools I use keeping all the (mangled, decompiled, and not even mine in the first place) code I point it at, and then using it in training to be hilarious.
And if it results in the next generation of AIs having more suspicious knowledge of proprietary software internals and better reverse engineering capabilities, then all the better.
It's the same as any service that makes you opt out of sucking up your data. It's a bad default, and it's not obvious to the average that it's even happening.