How does annihilationism posit a self?

In the context of Buddhist teachings, however, what matters is not the permanence or impermanence of the object of self-identification but the very fact of self-identification. Thus Buddhists view both sassatavada and ucchedavada as two varieties of atmavada... due to craving for non-being (vibhava-tanha), the desire to be completely annihilated at death. From the Buddhist point of view the reasoning for this may be conjectured as follows: because ucchedavada rejects survival, it tends to encourage man to lead a life without being burdened by a sense of moral responsibility or tormented by moral inhibitions. Therefore it abhors any prospect of after-death existence, as it implies the possibility of moral retribution

https://www.budsas.org/ebud/ebdha263.htm

Seems fair. I don't become nothing when I die, because I cannot identify it as "my" death.

Whether we can conventionally believe in self annihilation is not clear to me.

This is a better answer

I should just google these things. This source adds that annihilationists believe in a self now, and the eternalists one in the future.

It's because they hold that something existed for some time, 'a person'. The body is not the same now as what the body was when one was an infant but they say it's the same 'person'.

They posit an annihilation of the existent self only, the body they say will break up, heat will dissipate and consciousness is but a conditional property of matter which begins when person begins and ends when person ends.

They use the idea of self or 'person' to tie mind & body together in a messed up way where they treat mentality as if it is like smoke produced of rubbing two sticks but they don't conserve this property in any way unlike conservation of other material properties such as heat, mass, motion & etc and it apparently is made out of nothing and becomes nothing.

Of course it's philosophically impossible to somehow conserve or transform what only you could observe to something measurable by another person when you no longer exist...

Therefore they are called 'annihilationists, those who posit annihilation of an existent being', they make body & mind personable but won't be able to pin down the being as a truth & reality.

Without the idea of self they will have to admit that body & mind change as they persist and that cessation of mind is not evident and that it ought to be assumed to change as it persists even through the breakup of the body.

There's a very detailed description in DN 1.

Eternalism is the view that the self, atta or atman, is different from the body, and is eternal. When the body is destroyed, the self moves on to another body. But the self is never destroyed, is permanent and eternal.

Annihilation is the view where the self is identical with the body, and so it exists while the body exists and it is destroyed when the body is destroyed.

Or if someone holds the view that the self is a subtler body that exists when the physical body exists and will be destroyed with the destruction of the physical body, then that's also annihilationism.

Partial-eternalism is the view that either some beings are eternal (like God) while others are not, or some beings are eternal but could lose their immortality by corruption, or that consciousness or mind is eternal while body is not.

The above are all variants of self-view.

The Buddha taught that the self is a dependently originated emergent phenomena, a mental idea, that changes from time to time, depending on conditions. It's neither permanent nor standalone. Other things like body, mind, consciousness are all dependently originated conditioned phenomena.