Humans aren't eternal in the backwards direction- we have no memory of "before" we were born. To the best of my knowledge, Christianity doesn't claim that we existed before being born, but rather that God creates us at conception.
But here's my problem: you are not "you" until very late in life. An individual's personality really isn't formed until their late teens (if even then). Isn't this a problem for the idea of a soul? If a soul- that which gives us free will- is so fickle and malleable, how can it possibly be eternal? What makes me "me" doesn't seem to be that I was born as me, but rather that I grew into me- my genetics and surroundings have developed me this way.
Put it another way- if our soul is what goes on, which version of our soul is it? Is it the one we have when we are born? Or the one we have when we die? Or is it the best version of our soul that we ever have? Any answer here seems rather arbitrary to me.
Or perhaps the Christian claim is that the "soul" is entirely separable from the mind. Maybe your soul, your nature, doesn't change- but then we are left with the same question about the mind. And if the mind doesn't continue ad infinitum, then what can we say about the afterlife? That we do not think, that we are some ethereal being with broad prinicples but no personality? That doesn't make heaven sound so good (or hell sound so bad). Moreover, people do change, sometimes in fundamental ways. How can we say that the soul is eternal if its not even consistent in the brief glimpse we have of it on earth? Particularly if the attitude of the soul is the barometer of salvation, as is the case in most major religions. For example, what about someone like me, who once believed Christianity- and I truly did believe it, in every sense of the word- but has since ceased to believe? Which version of me is it that is eternal? Which me will be judged when I die?
Ultimately, I don't think these arguments about the nature of the soul are defeaters of Christianity. But I do think they're important to recognize, particularly in light of what I consider to be the best arguments for Christianity. Both the moral law argument and the question of purpose are very similar arguments- they ask the listener to apply strict logic to an idea that is "spiritual" in nature, and draw conclusions based on the fact that this logic contradicts the Atheist viewpoint. I think applying strict logic to the concept of a soul yields lackluster results for the Christian. Of course, the Christian can always make the argument that "we don't fully understand spiritual matters". But this sounds a lot like the Atheist who says "just because we don't understand the moral law, doesn't mean it's supernatural in nature."