While I have heard some people suggest something along these lines, I think most atheists simply believe that conscious experience simply ceases altogether upon death. While your criticism of this precise statement is perfectly valid - that it contains hidden premises which render it self-contradictory - I just don't think that this is what most atheists believe, at least those who have given that atheism a little thought.
The subjective experience of consciousness certainly seems to begin; it isn't like flicking a switch, it's not as though oneday we suddenly are conscious, but we certainly become conscious, there is no reason to think that we aren't to simply cease being conscious upon death.
Conscious is reducible, damage to our brain is capable of picking off aspects of consciousness individually. Particularly interesting are blind-sighted individuals, who are consciously blind to a portion of their visual field, though if forced to guess an image displayed in that blind portion, get the right answer a disproportionate amount of the time.
Anyway, if consciousness is reducible to smaller 'elements' then you have a problem, do bits of our consciousness individually die? do they individually pass on as part of this continuum of eternal consciousness?
Isn't that an oxymoron? I take it you mean hat consciousness survives bodily death, but then you have just posed the old mind-body problem, how does consciousness exist causally independent of the body?
Personally, the idea that consciousness is irreducible to the goings on in our brains is fine with me, but I cannot see how you can escape the fact that consciousness' existence seems dependent up the body/brain.