The desire to exist is to be present; to live life.
On the other hand, the desire to not exist is more complex.
In my opinion, not existing is physically impossible. You are here, right? But why? Because you were once born. You are capable of thinking, and that's the complex part.
Not existing is impossible as your mind always remains. When you think about how death is, even if you don't believe in reincarnation, you can't imagine how it feels to not exist. Why are you... Well... You? Your mind, why is it in your body specifically? Don't you feel like your mind will find another body once you die? You can't not exist, as your mind will always be in a body.

Now, what is the desire to not exist? It differs from the desire to stop existing.
The desire to not exist is simply that, not existing like you never did.
Don't mistake it with being lazy and not wanting to do anything.
If you don't exist, you can't suffer, you can't feel pain...
Only the saddest reasons lead you to this wish.
But... You will never experience it, or at least remember it; if you somehow achieve not existing, there's no going back, so you won't know how it feels as you don't exist. (Achieving 'not existing' technically is to stop existing, which, as I said, is different from the desire to not exist)
It's weird, I know.
When someone has the desire to not exist, at that moment they aren't feeling anything at all. Indifference, as well as many other reasons, leads you to this specific desire.
Still, not everyone desires it for the same reason.

As someone who has desired it, my reason is to not feel at all, as that negates any form of suffering. Either way, my desire to achieve absolute happiness is stronger.
In other words:
Lo deseo porque no quiero sentir.
That phrase alone describes a major part of who I am.

.                  -N. G. Y., 2025, The desire to not exist.

(Yes, N. G. Y are my initials) (I dare you to try to dox me with such small info) (Joking, pls don't dox me) (Welp, if you find a way to dox me, tell me privately and not to the whole internet.) (Good night).